Ken'ichiro TANAKA and Tomoaki OKAYAMA:
Numerical Methods with Variable Transformations,
Iwanami Shoten, Publishers, 2023.
(ISBN-13: 978-4-00-029860-5)
2021
Toshiyuki KATSURA (ed.), Tomoaki OKAYAMA,
Yoshihisa SATO, Makoto TAGAMI, Tohru WAKASA, Hideo HIROSE:
Differential equation for Students in the Science and Engineering Majors,
Baifukan, 2021.
(ISBN-13: 978-4-563-01158-1)
2017
Toshiyuki KATSURA (ed.), Yoshiaki OKAZAKI,
Tomoaki OKAYAMA, Natsuo SAITO,
Yoshihisa SATO, Makoto TAGAMI, Masayuki HIROKADO, Hideo HIROSE:
Calculus for Students in the Science and Engineering Majors,
Baifukan, 2017.
(ISBN-13: 978-4-563-01209-0)
2013
Tomoaki OKAYAMA:
Function aproximation, in Handbook of Applied Mathematics
(eds. Junkichi SATSUMA, Shin'ichi OISHI and Masaaki SUGIHARA),
Asakura Publishing, 2013, pp. 384–387.
(ISBN-13: 978-4-254-11141-5)
Papers (refereed)
202?
Tomoaki OKAYAMA, Ryota HARA and Shun'ichi GOTO:
Error analyses of Sinc-collocation methods for exponential decay
initial value problems, Nonlinear Theory and Its Applications, IEICE,
to appear in print.
2024
Tomoaki OKAYAMA and Shota OGAWA:
Improvement of selection formulas of mesh size and truncation numbers
for the DE-Sinc approximation and its theoretical error bound, Japan Journal of Industrial and Applied Mathematics,
Vol. 41 (2024), pp. 821–836.
[link]
2023
Tomoaki OKAYAMA and Yuta KAWAI:
Optimal selection formulas of mesh size and truncation numbers
for the double-exponential formula, JSIAM Letters,
Vol. 15 (2023), pp. 81–84.
[link]
Tomoaki OKAYAMA:
Sinc-collocation methods with consistent collocation points for Fredholm
integral equations of the second kind, Dolomites Research Notes on Approximation,
Vol. 16 (2023), pp. 63–74.
[link]
Tomoaki OKAYAMA and Ken'ichiro TANAKA:
Error analysis of approximation of derivatives by means of the Sinc
approximation for double-exponentially decaying functions, JSIAM Letters,
Vol. 15 (2023), pp. 5–8.
[link]
Tomoaki OKAYAMA and Katsuya HIROHATA:
Theoretical comparison of two conformal maps combined with the trapezoidal
formula for the semi-infinite integral of exponentially decaying functions,
JSIAM Letters,
Vol. 14 (2022), pp. 77–79.
[link] Paper Award in 2023, JSIAM
Tomoaki OKAYAMA:
Double-exponential formula for infinite integrals of unilateral rapidly
decreasing functions, JSIAM Letters,
Vol. 14 (2022), pp. 17–20.
[link]
2021
Tomoaki OKAYAMA and Tomoya SHIRAISHI:
Improvement of the conformal map combined with the Sinc approximation
for unilateral rapidly decreasing functions, JSIAM Letters,
Vol. 13 (2021), pp. 37–39.
[link]
Tomoaki OKAYAMA, Tomoki NOMURA and Saki TSURUTA:
New conformal map for the trapezoidal formula for infinite integrals of
unilateral rapidly decreasing functions, Journal of Computational and Applied Mathematics,
Vol. 389 (2021), 113354.
[link]
Tomoaki OKAYAMA and Shu HANADA:
A modified Stenger's quadrature formula for infinite integrals of unilateral
rapidly decreasing functions and its theoretical error bound, Mathematics and Computers in Simulation,
Vol. 186 (2021), pp. 3–18.
[link]
2020
Tomoaki OKAYAMA, Yuya SHINTAKU and Eisuke KATSUURA:
New conformal map for the Sinc approximation for exponentially decaying
functions over the semi-infinite interval, Journal of Computational and Applied Mathematics,
Vol. 373 (2020), 112358.
[link]
Tomoaki OKAYAMA and Chisei KUROGI:
Improvement of selection formulas of mesh size and truncation
numbers for the double-exponential formula, JSIAM Letters,
Vol. 12 (2020), pp. 13–16.
[link]
Tomoaki OKAYAMA and Ryota HAMADA:
Modified SE-Sinc approximation with boundary treatment over the semi-infinite
interval and its error bound, JSIAM Letters,
Vol. 11 (2019), pp. 5–7.
[link]
2018
Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA:
An optimal approximation formula for functions with singularities, Journal of Approximation Theory, Vol. 234 (2018), pp. 82–107.
[link]
Tomoaki OKAYAMA:
Theoretical analysis of a Sinc-Nyström method for Volterra
integro-differential equations and its improvement, Applied Mathematics and Computation, Vol. 324 (2018), pp. 1–15.
[link]
Tomoaki OKAYAMA:
Theoretical analysis of Sinc-collocation methods and
Sinc-Nyström methods for systems of initial value problems, BIT Numerical Mathematics, Vol. 58 (2018), pp. 199–220.
[link]
Tomoaki OKAYAMA:
Error estimates with explicit constants for the Sinc approximation over infinite intervals, Applied Mathematics and Computation, Vol. 319 (2018), pp. 125–137.
[link]
2017
Tomoaki OKAYAMA and Koichi MACHIDA:
Error estimate with explicit constants for the trapezoidal formula combined
with Muhammad–Mori's SE transformation for the semi-infinite interval, JSIAM Letters,
Vol. 9 (2017), pp. 45–47.
[link]
Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA:
Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces, IMA Journal of Numerical Analysis,
Vol. 37 (2017), pp. 861–904.
[link]
Tomoaki OKAYAMA:
Explicit error bound for modified numerical iterated integration by means of Sinc methods, Lecture Notes in Computer Science, Vol. 9582 (2016), pp. 202–217.
[link]
2015
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-Nyström methods for Volterra integral equations, Mathematics of Computation,
Vol. 84 (2015), pp. 1189–1215.
[link]
2014
Tomoaki OKAYAMA:
Modified Sinc-collocation methods for integral equations of the second kind
and their theoretical analysis (in Japanese), Bulletin of the Japan Society for Industrial and Applied Mathematics,
Vol. 24 (2014), pp. 110–114.
[link] Invited paper
(Introduction of the prize-winning paper in 2013,
JSIAM)
Tomoaki OKAYAMA:
Explicit error bound for the tanh rule and the DE formula for integrals with logarithmic singularity, JSIAM Letters,
Vol. 6 (2014), pp. 9–11.
[link]
2013
Tomoaki OKAYAMA:
Error estimates with explicit constants for Sinc quadrature and Sinc
indefinite integration over infinite intervals, Reliable Computing, Vol. 19 (2013), pp. 45–65.
[link]
Ken'ichiro TANAKA, Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
DE-Sinc methods have almost the same convergence property
as SE-Sinc methods even for a family of functions
fitting the SE-Sinc methods.
Part II: Indefinite integration, Numerische Mathematik,
Vol. 125 (2013), pp. 545–568.
[link]
Tomoaki OKAYAMA, Ken'ichiro TANAKA, Takayasu MATSUO and Masaaki SUGIHARA:
DE-Sinc methods have almost the same convergence property
as SE-Sinc methods even for a family of functions
fitting the SE-Sinc methods.
Part I: Definite integration and function approximation, Numerische Mathematik,
Vol. 125 (2013), pp. 511–543.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for Sinc approximation,
Sinc quadrature and Sinc indefinite integration, Numerische Mathematik,
Vol. 124 (2013), pp. 361–394.
[link]
Tomoaki OKAYAMA:
A note on the Sinc approximation with boundary treatment, JSIAM Letters,
Vol. 5 (2013), pp. 1–4.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
On boundedness of the condition number of the coefficient matrices appearing in Sinc-Nyström methods for Fredholm integral equations of the second kind, JSIAM Letters,
Vol. 3 (2011), pp. 81–84.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Improvement of a Sinc-collocation method for Fredholm integral equations of the second kind, BIT Numerical Mathematics,
Vol. 51 (2011), pp. 339–366.
[link]
2010
Naoya YAMANAKA, Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast verified automatic integration algorithm using double exponential formula, Nonlinear Theory and Its Applications, IEICE,
Vol. 1 (2010), pp. 119–132.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Sinc-collocation methods for weakly singular Fredholm integral equations
of the second kind, Journal of Computational and Applied Mathematics,
Vol. 234 (2010), pp. 1211–1227.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for the tanh rule and the DE formula
for indefinite integrals, JSIAM Letters,
Vol. 2 (2010), pp. 13–16.
[link]
Naoya YAMANAKA, Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast verified automatic integration algorithm
using double exponential formula, Sûrikaisekikenkyûsho Kôkyûroku,
No. 1638
"Numerical Analysis: Theory, Methods and Applications,"
pp. 146–158, 2009.
[link]
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Sinc methods for integral equations of the second kind and their
theoretical analysis (in Japanese), Sûrikaisekikenkyûsho Kôkyûroku,
No. 1638
"Numerical Analysis: Theory, Methods and Applications,"
pp. 38–55, 2009.
[link]
(Review paper of my main researches in 2007–2008)
Refereed Conference Proceedings
2022
Tomoaki OKAYAMA:
Corrected error bound for the real gamma function using the DE formula,
Proceedings of the 2022 International Symposium on Nonlinear Theory and Its
Applications, 2022, pp. 593–596.
[link]
2020
Tomoaki OKAYAMA and Ryota HARA:
Sinc-collocation methods for exponential decay initial value problems,
Proceedings of the 2020 International Symposium on Nonlinear Theory and Its
Applications, 2020, pp. 509–512.
[link]
2018
Naoya YAMANAKA, Tomoaki OKAYAMA and Shin'ichi OISHI:
Numerical algorithm for sine integral with verification,
Proceedings of The 37th JSST Annual International Conference on Simulation Technology, 2018, pp. 129–131.
Ryota HARA and Tomoaki OKAYAMA:
Improvement of Sinc-Nyström methods for initial value problems,
Proceedings of the 2018 International Symposium on Nonlinear Theory and Its
Applications, 2018, pp. 651–654.
[link]
2017
Naoya YAMANAKA, Tomoaki OKAYAMA and Shin'ichi OISHI:
Verified algorithm for gamma function using double exponential formula and its applications,
Proceedings of The 36th JSST Annual International Conference on Simulation Technology, 2017, pp. 222–225.
Ryota HARA and Tomoaki OKAYAMA:
Explicit error bound for Muhammad–Mori's SE-Sinc indefinite integration
formula over the semi-infinite interval,
Proceedings of the 2017 International Symposium on Nonlinear Theory and Its
Applications, 2017, pp. 677–680.
[link]
Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA:
Potential theoretic approach to design of accurate numerical integration
formulas in weighted Hardy spaces, Approximation Theory XV: San Antonio 2016 (eds. Gregory E. FASSHAUER and Larry L. SCHUMAKER), Springer Cham, 2017, pp. 335–360.
[link]
2016
Naoya YAMANAKA, Tomoaki OKAYAMA and Shin'ichi OISHI:
Verified error bounds for the real gamma function using double exponential formula over semi-infinite interval, Mathematical Aspects of Computer and Information Sciences (eds. Ilias S. KOTSIREAS, Siegfried M. RUMP and Chee K. YAP), Springer Cham, 2016, pp. 224–228.
[link]
2015
Tomoaki OKAYAMA:
Improvement of a Sinc-collocation method for Fredholm integro-differential
equations,
Proceedings of the International Conference on Numerical Analysis
and Applied Mathematics 2014 (ICNAAM-2014),
AIP Conference Proceedings,
Vol. 1648 (2015), No. 390008.
[link]
2014
Xuefeng LIU, Tomoaki OKAYAMA and Shin'ichi OISHI:
High-precision eigenvalue bound for the Laplacian with singularities, Computer Mathematics (eds. Ruyong FENG, Wen-shin LEE and Yosuke SATO),
Springer Berlin Heidelberg, 2014, pp. 311–323.
[link]
2009
Naoya YAMANAKA, Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast automatic integration algorithm using double exponential
formula based on verification theory,
Proceedings of
the 24th International Technical Conference on Circuits/Systems, Computers
and Communications,
2009, pp. 161–164.
[link]
Technical Reports (preprints submitted to journals)
2023
Tomoaki OKAYAMA, Ryota HARA and Shun'ichi GOTO:
Error analyses of Sinc-collocation methods for exponential decay
initial value problems, arXiv:2306.15175
[math.NA], Jun 2023.
Tomoaki OKAYAMA and Shota OGAWA:
Improvement of selection formulas of mesh size and truncation numbers
for the DE-Sinc approximation and its theoretical error bound, arXiv:2303.08334
[math.NA], Mar 2023.
The improved version has been published in Japan Journal of Industrial and Applied Mathematics.
Tomoaki OKAYAMA:
Sinc-collocation methods with consistent collocation points for Fredholm
integral equations of the second kind, arXiv:2301.12692
[math.NA], Jan 2023.
The improved version has been published in Dolomites Research Notes on Approximation.
Talks in International Conferences
2023
Tomoaki OKAYAMA:
Approximate formula for indefinite convolutions by the DE-Sinc method,
10th International Congress on Industrial and Applied Mathematics
(ICIAM 2023), Tokyo, Japan (Aug 20–25, 2023).
Tomoaki OKAYAMA, Ryota HARA and Shun'ichi GOTO:
Error analyses of Sinc-collocation methods for exponential decay initial
value problems,
Second International Conference on Mathematical And Computational Modelling,
Approximation and Simulation (MACMAS 2023), Torino, Piedmont, Italy
(May 29–Jun. 1, 2023), abstracts p. 54.
2022
Tomoaki OKAYAMA:
Corrected error bound for the real gamma function using the DE formula,
The 2022 International Symposium on Nonlinear Theory and Its Applications
(NOLTA2022), Croatia (Virtual online conference) (Dec. 12–15, 2022).
Tomoaki OKAYAMA:
Sinc-collocation methods with consistent collocation points for Fredholm
integral equations of the second kind,
International Conference on Functional Analysis, Approximation Theory
and Numerical Analysis (FAATNA20>22),
Matera, Basilicata, Italy (Jul. 5–8, 2022),
abstracts p. 36.
2021
Tomoaki OKAYAMA and Shota OGAWA:
Improvement of selection formulas of mesh size and truncation number
for the DE-Sinc approximation and its theoretical error bound,
The 19th International Symposium on Scientific Computing, Computer
Arithmetic, and Verified Numerical Computations (SCAN2020),
Hungary (Virtual online conference) (Sep. 13–15, 2021),
abstracts pp. 57–58.
Tomoaki OKAYAMA:
Yet another Sinc indefinite integration formula,
5th Dolomites Workshop on Constructive Approximation and Applications
(DWCAA21), Italy (Virtual online conference) (Sep. 6–10, 2021),
abstracts p. 5 in the session
"Numerical integration, integral equations and transforms".
2020
Tomoaki OKAYAMA and Ryota HARA:
Sinc-collocation methods for exponential decay initial value problems,
The 2020 International Symposium on Nonlinear Theory and Its Applications
(NOLTA2020), Japan (Virtual online conference) (Nov. 16–20, 2020),
abstracts pp. 52–53.
2019
Tomoaki OKAYAMA and Shu HANADA:
A modified Stenger's quadrature formula for infinite integrals of unilateral
rapidly decreasing functions and its theoretical error bound,
Mathematical and Computational Modelling, Approximation and Simulation 2019
(MACMAS 2019),
Granada, Andalusia, Spain (Sep. 9–11, 2019), abstracts p. 19.
2018
Naoya YAMANAKA (talker), Tomoaki OKAYAMA
and Shin'ichi OISHI:
Numerical algorithm for sine integral with verification,
The 37th JSST Annual International Conference on Simulation Technology
(JSST2018), Muroran, Hokkaido, Japan (Sep. 18–20, 2018).
Fuminori TATSUOKA (talker), Tomoaki OKAYAMA, Shao-Liang ZHANG and Masaaki SUGIHARA:
A note on computing the pth root of Sinc matrices,
16th International Conference of Numerical Analysis and Applied Mathematics
(ICNAAM 2018),
Rhodes, South Aegean, Greece (Sep. 13–18, 2018).
Naoya YAMANAKA (talker), Tomoaki OKAYAMA
and Shin'ichi OISHI:
Verified algorithm for the sine integral,
The 18th International Symposium on Scientific Computing,
Computer Arithmetic, and Verified Numerical Computations
(SCAN 2018), Tokyo, Japan (Sep. 10–15, 2018),
abstracts pp. 170–171.
Ryota HARA (talker) and Tomoaki OKAYAMA:
Improvement of Sinc-Nyström methods for initial value problems,
The 2018 International Symposium on Nonlinear Theory and Its Applications
(NOLTA2018), Tarragona, Catalonia, Spain (Sep. 2–6, 2018),
abstracts p. 62.
Tomoaki OKAYAMA, Yuya SHINTAKU and Eisuke KATSUURA:
New conformal map for the Sinc approximation for exponentially-decaying functions over the semi-infinite interval,
Numerical Analysis and Scientific Computation with Applications (NASCA 2018),
Kalamata, Messenia, Greece (Jul. 2–6, 2018), abstracts p. 81.
2017
Ryota HARA (talker) and Tomoaki OKAYAMA:
Explicit error bound for Muhammad–Mori's SE-Sinc indefinite integration
formula over the semi-infinite interval,
The 2017 International Symposium on Nonlinear Theory and Its Applications
(NOLTA2017), Cancún, Quintana Roo, Mexico (Dec. 4–7, 2017),
abstracts p. 59.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA
and Shin'ichi OISHI:
Verified algorithm for gamma function using double exponential formula and its applications,
The 36th JSST Annual International Conference on Simulation Technology
(JSST2017), Tokyo, Japan (Oct. 25–27, 2017).
Naoya YAMANAKA (talker), Tomoaki OKAYAMA
and Shin'ichi OISHI:
Verified error bounds for the modified Bessel function of the second kind
using double exponential formula over semi-infinite interval,
International Workshop on Numerical Verification and its Applications 2017
(INVA 2017), Miyakojima, Okinawa, Japan (Mar. 14–18, 2017). Invited talk
Tomoaki OKAYAMA:
Recent development of variable transformations combined with the trapezoidal
formula,
International Workshop on Numerical Verification and its Applications 2017
(INVA 2017), Miyakojima, Okinawa, Japan (Mar. 14–18, 2017). Invited talk
2016
Ken'ichiro TANAKA (talker), Tomoaki OKAYAMA and Masaaki SUGIHARA:
Potential theoretic approach to approximation in weighted Hardy spaces,
The 11th East Asia SIAM Conference (EASIAM 2016),
Macao, Macao SAR, China (Jun. 20–22, 2016), abstracts pp. 57–58.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA,
Shin'ichi OISHI and Yukari MAKI:
Verified algorithm for the modified Bessel function of the second kind,
5th European Seminar on Computing (ESCO 2016),
Pilsen, Pilsen, Czech Republic (Jun. 5–10, 2016), abstracts p. 265.
Tomoaki OKAYAMA:
Error estimates with explicit constants for the Sinc approximation
over infinite intervals,
5th European Seminar on Computing (ESCO 2016),
Pilsen, Pilsen, Czech Republic (Jun. 5–10, 2016), abstracts p. 193.
2015
Naoya YAMANAKA (talker), Tomoaki OKAYAMA
and Shin'ichi OISHI:
Verified error bounds for the real gamma function using
double exponential formula over semi-infinite interval,
6th International Conference on Mathematical Aspects of Computer and
Information Sciences (MACIS 2015),
Berlin, Berlin, Germany (Nov. 11–13, 2015).
Tomoaki OKAYAMA:
Explicit error bound for modified numerical iterated integration
by means of Sinc methods,
6th International Conference on Mathematical Aspects of Computer and
Information Sciences (MACIS 2015),
Berlin, Berlin, Germany (Nov. 11–13, 2015).
Ken'ichiro TANAKA (talker), Tomoaki OKAYAMA and Masaaki SUGIHARA:
Potential theoretic approach to design an optimal formula for function approximation in a weighted Hardy space,
New Directions in Numerical Computation,
Oxford, Oxfordshire, UK (Aug. 25–28, 2015), abstracts p. 45.
2014
Tomoaki OKAYAMA:
Improvement of a Sinc-collocation method for Fredholm integro-differential
equations,
12th International Conference of Numerical Analysis and Applied Mathematics
(ICNAAM 2014),
Rhodes, South Aegean, Greece (Sep. 22–28, 2014).
2013
Tomoaki OKAYAMA:
Sinc-collocation methods for Volterra integro-differential equations,
International Conference on Scientific Computation and Differential Equations
2013 (SciCADE 2013),
Valladolid, Castile and León, Spain (Sep. 16–20, 2013),
abstracts pp. 117–118.
Tomoaki OKAYAMA:
Theoretical analysis of a Sinc-Nyström method for Volterra
integro-differential equations and its improvement,
18th International Conference
Mathematical Modelling and Analysis (MMA2013)
and Fourth International Conference
Approximation Methods and Orthogonal Expansions (AMOE2013),
Tartu, Tartu County, Estonia (May 27–30, 2013), abstracts p. 88.
2012
Tomoaki OKAYAMA:
Error estimates with explicit constants for Sinc quadrature
and Sinc indefinite integration over infinite intervals,
The 15th GAMM-IMACS International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics
(SCAN 2012), Akademgorodok, Novosibirsk, Russia (Sep. 23–29, 2012),
abstracts pp. 125–126.
Tomoaki OKAYAMA:
Sinc-collocation method for initial value problems
by means of the DE transformation,
The 16th International Congress on Computational and Applied Mathematics
(ICCAM2012), Ghent, East Flanders, Belgium (Jul. 9–13, 2012),
abstracts p. 75.
2011
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-collocation methods for weakly singular
Volterra integral equations of the second kind,
24th Biennial Conference on Numerical Analysis (NACONF 2011),
Glasgow, Scotland, UK (Jun. 28–Jul. 1, 2011),
abstracts pp. 37–38.
2010
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
A posteriori error estimates of Sinc-Nyström methods
for Fredholm integral equations of the second kind,
The 14th GAMM-IMACS International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics
(SCAN 2010), Lyon, Rhône, France (Sep. 27–30, 2010),
abstracts pp. 110–111.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-Nyström methods for Volterra integral
equations of the second kind,
The 4th International Conference Computational Methods in Applied Mathematics
(CMAM-4), Będlewo, Poznań County, Poland (Jun. 20–26, 2010),
abstracts p. 66.
2009
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Modified Sinc-collocation methods for Volterra integral equations
of the second kind and their theoretical analysis,
The 14th International Congress on Computational and Applied Mathematics
(ICCAM2009), Lara, Antalya, Turkey (Sep. 29–Oct. 2, 2009),
abstracts p. 194.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Improvement of a Sinc-collocation method for Fredholm integral equations
of the second kind,
2nd Dolomites Workshop on Constructive Approximation and Applications
(DWCAA09), Alba di Canazei, Trento, Italy (Sep. 4–9, 2009),
abstracts p. 73.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast automatic integration algorithm using double exponential formula
based on verification theory,
The 24th International Technical Conference on Circuits/Systems, Computers
and Communications (ITC-CSCC 2009), Jeju, Jeju Island, Korea
(Jul. 5–8, 2009).
Naoya YAMANAKA (talker), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast automatic integration algorithm using double exponential formula,
The 2nd International Conference on Mathematical Modelling and
Computation and The 5th East Asia SIAM Conference,
Bandar Seri Begawan, Brunei Muara, Brunei
(Jun. 8–11, 2009), abstracts p. 51.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for Sinc approximation,
Sinc quadrature and Sinc indefinite integration,
International Workshop on Numerical Verification and its Applications 2009
(INVA2009), Miyakojima, Okinawa, Japan (Mar. 22–29, 2009).
2008
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Approximate formulae for fractional derivatives by means of Sinc methods,
International Conference on Applied Mathematics and Approximation Theory 2008
(AMAT2008), Memphis, Tennessee, USA (Oct. 11–13, 2008),
abstracts p. 50.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Sinc-collocation methods for weakly singular Fredholm integral equations
of the second kind,
The 13th International Congress on Computational and Applied Mathematics
(ICCAM2008), Ghent, East Flanders, Belgium (Jul. 7–11, 2008),
abstracts p. 82.
Talks in Domestic Conferences (in Japanese)
2024
Kosei ARAKAWA (talker) and Tomoaki OKAYAMA:
Improvement of theoretical error bounds of the SE and DE formulas for
integrals with logarithmic singularity over the finite interval,
JSIAM 2024 Meeting of the Union of Research Activity Groups,
Nagaoka (Mar. 4–6, 2024).
Ryo KAMIGAKI (talker) and Tomoaki OKAYAMA:
Theoretical error bounds of the SE and DE formulas for integrals of
polynomially decaying functions with logarithmic singularity over the
semi-infinite interval,
JSIAM 2024 Meeting of the Union of Research Activity Groups,
Nagaoka (Mar. 4–6, 2024).
Eita YABUMOTO and Tomoaki OKAYAMA:
Theoretical error bounds of the SE and DE formulas for integrals of
exponentially decaying functions with logarithmic singularity over the
semi-infinite interval,
JSIAM 2024 Meeting of the Union of Research Activity Groups,
Nagaoka (Mar. 4–6, 2024).
2023
Tadatoshi KOSAKA (talker) and Tomoaki OKAYAMA:
Approximation of derivatives over the finite interval by means of the
Sinc approximation combined with the DE transformation and its theoretical
error estimate,
JSIAM 2023 Meeting of the Union of Research Activity Groups,
Okayama (Mar. 8–10, 2023).
Saya TSUCHIYAMA (talker) and Tomoaki OKAYAMA:
Approximation of derivatives over the semi-infinite interval by means of the
Sinc approximation combined with the DE transformation and its theoretical
error estimate,
JSIAM 2023 Meeting of the Union of Research Activity Groups,
Okayama (Mar. 8–10, 2023).
2022
Tomoaki OKAYAMA and Ken'ichiro TANAKA:
Error estimate of approximation of derivatives by means of the Sinc
approximation for double-exponentially decaying functions,
The 2022 Annual Meeting of JSIAM,
Sapporo (Sep. 8–10, 2022), abstracts G2-1-2.
Yuta KAWAI (talker) and Tomoaki OKAYAMA:
Improvement of selection formulas of mesh size and truncation numbers for
the DE formula and its theoretical error estimate,
JSIAM 2022 Meeting of the Union of Research Activity Groups,
Online (Mar. 8–9, 2022).
2021
Shota OGAWA (talker) and Tomoaki OKAYAMA:
Improvement of selection formulas of mesh size and truncation numbers for
the DE-Sinc approximation and its theoretical error estimate,
JSIAM 2021 Meeting of the Union of Research Activity Groups,
Online (Mar. 4–5, 2021).
Katsuya HIROHATA (talker) and Tomoaki OKAYAMA:
Theoretical comparison of two conformal maps combined with the trapezoidal
formula for the semi-infinite integral of exponentially decaying functions,
JSIAM 2020 Meeting of the Union of Research Activity Groups,
Online (Mar. 4–5, 2021).
2020
Tomoaki OKAYAMA:
Double-exponential formula for infinite integrals of unilateral rapidly
decreasing functions,
The 2020 Annual Meeting of JSIAM,
Online (Sep. 8–10, 2020), abstracts pp. 103–104.
Tomoya SHIRAISHI (talker) and Tomoaki OKAYAMA:
Improvement of the SE-Sinc approximation for unilateral rapidly decreasing
functions and its theoretical error estimate,
JSIAM 2020 Meeting of the Union of Research Activity Groups,
Tokyo (Mar. 4–5, 2020).
Tomoki NOMURA (talker) and Tomoaki OKAYAMA:
Improvement of theoretical error estimate for the SE formula by Tsuruta
et al. for infinite integrals of unilateral rapidly decreasing functions,
JSIAM 2020 Meeting of the Union of Research Activity Groups,
Tokyo (Mar. 4–5, 2020).
2019
Tomoaki OKAYAMA and Chisei KUROGI:
Improvement of theoretical error estimate of the double-exponential formula,
The 2019 Annual Meeting of JSIAM,
Tokyo (Sep. 3–5, 2019), abstracts pp. 323–324.
Tomoaki OKAYAMA:
On developments in numerical methods with variable transformations,
Meetings of Numerical Analysis 2019, Tokyo (Jun. 9, 2019). Invited talk
2018
Ryota HARA (talker) and Tomoaki OKAYAMA:
Error analysis of the Sinc-Nyström methods for initial value problems of ordinary differential equations,
The 47th Numerical Analysis Symposium 2018
(NAS2018), Awara (Jun. 6–8, 2018), abstracts pp. 82–85.
Saki TSURUTA (talker), Shu HANADA and Tomoaki OKAYAMA:
Improvement of the SE formula for infinite integrals of unilateral rapidly decreasing functions and its theoretical error estimate,
JSIAM 2018 Meeting of the Union of Research Activity Groups,
Suita (Mar. 15–16, 2018).
Ryota HARA (talker) and Tomoaki OKAYAMA:
Improvement of the DE-Sinc-Nyström method for initial value problems of ordinary differential equations,
JSIAM 2018 Meeting of the Union of Research Activity Groups,
Suita (Mar. 15–16, 2018).
2017
Ryota HARA (talker) and Tomoaki OKAYAMA:
Improvement of the SE-Sinc-Nyström method for initial value problems of ordinary differential equations,
The 2017 Annual Meeting of JSIAM,
Tokyo (Sep. 6–8, 2017), abstracts pp. 387–388.
Tomoaki OKAYAMA and Ryota HAMADA:
Improvement of the SE-Sinc approximation with boundary treatment over the semi-infinite interval and its error estimate,
The 2017 Annual Meeting of JSIAM,
Tokyo (Sep. 6–8, 2017), abstracts pp. 105–106.
Yuya SHINTAKU (talker), Eisuke KATSUURA and Tomoaki OKAYAMA:
Improvement of the SE transformation for the Sinc approximation
over the semi-infinite interval and its theoretical error estimate,
JSIAM 2017 Meeting of the Union of Research Activity Groups,
Chôfu (Mar. 6–7, 2017).
Ryota HARA (talker) and Tomoaki OKAYAMA:
Error estimate with explicit constants for Muhammad–Mori's SE-Sinc indefinite
integration formula,
JSIAM 2017 Meeting of the Union of Research Activity Groups,
Chôfu (Mar. 6–7, 2017).
2016
Ken'ichiro TANAKA (talker), Tomoaki OKAYAMA and Masaaki SUGIHARA:
Designing a highly accurate numerical integration formula on a weighted Hardy space,
The 2016 Annual Meeting of JSIAM,
Kitakyushu (Sep. 12–14, 2016), abstracts pp. 50–51.
Kosuke SUGITA (talker), Masaaki SUGIHARA, Ken'ichiro TANAKA and Tomoaki OKAYAMA:
Comparison of two optimal function approximation formulas on a weighted Hardy space on an eye-shaped domain,
The 2016 Annual Meeting of JSIAM,
Kitakyushu (Sep. 12–14, 2016), abstracts pp. 48–49.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA, Shin'ichi OISHI and Yukari MAKI:
Verified algorithm for the modified Bessel function using the double exponential formula,
JSIAM 2016 Meeting of the Union of Research Activity Groups,
Kobe (Mar. 4–5, 2016).
Ayato YAMAMOTO (talker), Tomoaki OKAYAMA and Teruo TANAKA:
Ranking of teams in a Kendo team tournament by the two step method,
The 19th Symposium of Setouchi-rim JSIAM Local Research Group,
Amagase (Jan. 8–9, 2016),
abstracts pp. 52–55.
2015
Tomoaki OKAYAMA and Yuki KOJYO:
A note on the trapezoidal rule combined with the polar coordinates transformation and the DE transformation for two-dimensional infinite integration,
The 2015 Annual Meeting of JSIAM,
Kanazawa (Sep. 9–11, 2015),
abstracts annual2015_29_2_0754.pdf (2 pages).
Ken'ichiro TANAKA (talker), Tomoaki OKAYAMA and Masaaki SUGIHARA:
Designing an optimal interpolation formula on a weighted Hardy space using potential theory,
The 44th Numerical Analysis Symposium 2015
(NAS2015), Koshu (Jun. 8–10, 2015), abstracts pp. 9–12.
Tomoaki OKAYAMA and Koichi MACHIDA:
Error estimate with explicit constants for the SE formula of Muhammad–Mori,
JSIAM 2015 Meeting of the Union of Research Activity Groups,
Tokyo (Mar. 6–7, 2015).
2013
Tomoaki OKAYAMA:
A posteriori error estimates of Sinc-collocation methods
for Fredholm integral equations of the second kind,
Joint Conference on Applied Mathematics,
Seta (Dec. 19–21, 2013), abstracts pp. 192–197.
Tomoaki OKAYAMA, Ken'ichiro TANAKA:
On convergence of DE-Sinc methods for the function classes
for which SE-Sinc methods are suitable,
The 2013 Annual Meeting of JSIAM,
Fukuoka (Sep. 9–11, 2013), abstracts pp. 130–131.
Tomoaki OKAYAMA:
Sinc-Nyström methods for Fredholm integro-differential equations
and their theoretical analysis,
The 42st Numerical Analysis Symposium 2013
(NAS2013), Matsuyama (Jun. 12–14, 2013), abstracts pp. 136–139.
Tomoaki OKAYAMA:
Error estimates with explicit constants for the tanh rule and the DE formula
for integrals with logarithmic singularity,
JSIAM 2013 Meeting of the Union of Research Activity Groups,
Tokyo (Mar. 14–15, 2013).
2012
Tomoaki OKAYAMA:
On error estimate for the double-exponential formula,
Three JSIAM Research Activity Groups Cooperative Seminar on "Applied Mathematics,"
Tokyo (Dec. 25, 2012), abstracts pp. 63–82.
Tomoaki OKAYAMA:
Error estimates with explicit constants for numerical iterated integration by means of Sinc quadrature and Sinc indefinite integration,
Joint Conference on Applied Mathematics,
Seta (Dec. 20–22, 2012), abstracts pp. 190–193.
Tomoaki OKAYAMA:
Error estimates with explicit constants for the Sinc approximation
over infinite intervals,
The 2012 Annual Meeting of JSIAM,
Wakkanai (Aug. 28–Sep. 2, 2012), abstracts pp. 251–252.
Tomoaki OKAYAMA:
Sinc-collocation methods for initial value problems of fractional
differential equations,
The 41st Numerical Analysis Symposium 2012
(NAS2012), Ikaho (Jun. 6–8, 2012), abstracts pp. 58–61.
Tomoaki OKAYAMA:
Sinc-collocation methods for Volterra integro-differential equations
and their theoretical analysis,
JSIAM 2012 Meeting of the Union of Research Activity Groups,
Fukuoka (Mar. 8–9, 2012).
2011
Tomoaki OKAYAMA:
Improvement and theoretical analysis of Sinc-Nyström methods
for Volterra integro-differential equations,
Joint Conference on Applied Mathematics,
Seta (Dec. 15–17, 2011), abstracts pp. 220–223.
Tomoaki OKAYAMA:
Numerical integration formula with a variable transformation
and its developments,
The 4th Mathematical Science Seminar,
Kunitachi (Nov. 16, 2011).
Takashi USHIMA, Tomoaki OKAYAMA and Masaaki SUGIHARA (talker):
Optimal function approximation formula based on the generalized Ganelius theorem,
Workshop in Research Institute for Mathematical Sciences:
"The latest developments in theory and application on scientific computation,"
Kyoto (Oct. 25–27, 2011), abstracts pp. 30–32.
Tomoaki OKAYAMA:
Modified Sinc-collocation methods for Fredholm integro-differential equations
and their theoretical analysis,
The 40th Numerical Analysis Symposium 2011
(NAS2011), Toba (Jun. 20–22, 2011), abstracts pp. 17–20.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
On boundedness of the condition number of coefficient matrices
generated in Sinc-Nyström methods
for Fredholm integral equations of the second kind,
JSIAM 2011 Meeting of the Union of Research Activity Groups,
Chôfu (Mar. 7–8, 2011).
Tomoaki OKAYAMA:
On tuning parameters of Sinc-Nyström methods
for integral equations of the second kind,
Kunitachi One-Day Symposium on Numerical Analysis and Related Topics,
Kunitachi (Jan. 29, 2011).
2010
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Comparison among a variety of Sinc schemes for initial value problems
of ODEs,
Joint Conference on Applied Mathematics,
Seta (Dec. 16–18, 2010), abstracts pp. 163–168.
Tomoaki OKAYAMA:
Theoretical analysis of Sinc schemes
for integral equations of the second kind,
UT Numerical Analysis Seminar (UTNAS), Tokyo (Oct. 26, 2010).
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for the SE formula
and DE formula over infinite intervals,
The 2010 Annual Meeting of JSIAM,
Tokyo (Sep. 6–9, 2010), abstracts pp. 95–96.
Tomoaki OKAYAMA, Ken'ichiro TANAKA, Takayasu MATSUO and Masaaki SUGIHARA:
Error analysis of the DE formula for a class of functions
for which the tanh rule is suitable,
The 39th Numerical Analysis Symposium 2010
(NAS2010), Toba (May 26–28, 2010), abstracts pp. 29–32.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
A priori and a posteriori error estimates of Sinc-Nyström methods
for Fredholm integral equations of the second kind,
JSIAM 2010 Meeting of the Union of Research Activity Groups,
Tsukuba (Mar. 8–9, 2010).
2009
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for Sinc-Nyström methods
for Fredholm integral equations of the second kind,
Joint Conference on Applied Mathematics,
Seta (Dec. 17–19, 2009), abstracts pp. 129–132.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
A fast automatic integration algorithm using double exponential formula
based on verification theory,
The 38th Numerical Analysis Symposium 2009 (NAS2009),
Higashiizu (Jun. 15–17, 2009),
abstracts pp. 5–8.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for Sinc approximation,
Sinc quadrature and Sinc indefinite integration,
JSIAM 2009 Meeting of the Union of Research Activity Groups,
Kyoto (Mar. 7–8, 2009).
2008
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-Nyström methods
for Volterra integral equations of the second kind,
Joint Conference on Applied Mathematics,
Seta (Dec. 15–17, 2008), abstracts pp. 193–196.
Naoya YAMANAKA (talker), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
Improvement of fast verified automatic integration using double
exponential formula,
Workshop in Research Institute for Mathematical Sciences:
"Numerical Analysis: Theory, Methods, and Applications,"
Kyoto (Nov. 12–14, 2008), abstracts pp. 29–30.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Sinc methods for integral equations of the second kind and their
theoretical analysis,
Workshop in Research Institute for Mathematical Sciences:
"Numerical Analysis: Theory, Methods, and Applications,"
Kyoto (Nov. 12–14, 2008), abstracts pp. 26–28.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-Nyström methods
for Fredholm integral equations of the second kind,
The 2008 Annual Meeting of JSIAM,
Kashiwa (Sep. 17–19, 2008), abstracts pp. 397–398.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Uniform approximation of fractional derivatives by means of Sinc methods,
The 37th Numerical Analysis Symposium 2008
(NAS2008), Semboku (Jun. 12–14, 2008), abstracts pp. 115–118.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of Sinc-collocation methods
for integral equations of the second kind
and applications of the DE transformation,
JSIAM 2008 Meeting of the Union of Research Activity Groups,
Hachiôji (Mar. 3–4, 2008).
2007
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of numerical methods based on Sinc-collocation
for integral equations of the second kind,
Joint Conference on Applied Mathematics,
Seta (Dec. 17–19, 2007), abstracts pp. 250–253.
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Theoretical analysis of the Sinc numerical method
for weakly singular integral equations of the second kind,
The 2007 Annual Meeting of JSIAM,
Sapporo (Sep. 15–17, 2007), abstracts pp. 332–333. Talk Award in 2007, JSIAM
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Sinc numerical method for Fredholm integral equations of the second kind
with a weakly singular kernel,
The 36th Numerical Analysis Symposium 2007
(NAS2007), Atami (Jun. 19–21, 2007), abstracts pp. 105–108.
2006
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Approximate formula for indefinite convolutions by the DE-Sinc method,
The 2006 Annual Meeting of JSIAM,
Tsukuba (Sep. 16–18, 2006), abstracts pp. 298–299.
2005
Tomoaki OKAYAMA and Sunao MURASHIGE:
Numerical calculation of fractional derivatives using automatic
differentiation and double exponential formula,
The 34th Numerical Analysis Symposium 2005
(NAS2005), Hamamatsu (Jun. 28–30, 2005), abstracts pp. 25–28.
Posters in International Conferences
2017
Ryota HARA (presenter) and Tomoaki OKAYAMA:
Explicit error bound for Muhammad–Mori's SE-Sinc indefinite integration
formula over the semi-infinite interval,
The 2017 International Symposium on Nonlinear Theory and Its Applications
(NOLTA2017), Cancún, Quintana Roo, Mexico (Dec. 4–7, 2017). Finalist in NOLTA2017 Student Paper Award
Naoya YAMANAKA (presenter), Tomoaki OKAYAMA and Shin'ichi OISHI:
Verified error bounds for the gamma function using double
exponential formula,
International Workshop on Industrial Mathematics / ICIAM Board Meeting 2017 (iwimath17),
Burjassot, València (May 18–19 / 20, 2017).
Posters in Domestic Conferences (in Japanese)
2009
Tomoaki OKAYAMA, Takayasu MATSUO and Masaaki SUGIHARA:
Error estimates with explicit constants for numerical indefinite integration
using the tanh rule and the DE formula,
The 38th Numerical Analysis Symposium 2009 (NAS2009),
Higashiizu (Jun. 15–17, 2009),
abstracts pp. 63–66.
Naoya YAMANAKA (presenter), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
Improvement of fast verified automatic integration using double
exponential formula,
The 2nd High-Tech Research Symposium, Ôkubo (Jan. 17, 2009).
2008
Naoya YAMANAKA (presenter), Tomoaki OKAYAMA, Shin'ichi OISHI and Takeshi OGITA:
Fast verified automatic integration using double exponential formula,
The 4th Symposium on "Innovation of Simulation Technology and Construction of Bases for Practical Applications,"
Mita (Nov. 12, 2008).