[Ooura's Mathematical Software | Fast PI(=3.14...) Computation] (Japanese)
Takuya Ooura
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My research interest is numerical analysis.

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___Personal History
  • Date of Birth: Mar 19, 1969
  • Place of Birth: Fukui Prefecture, Japan
  • 1987: Graduated Hokuriku High School (Fukui Prefecture)
  • 1992: Graduated School of Science of Nagoya University
  • 1994: Master of Engineering, Department of Applied Physics, School of Engineering, The University of Tokyo
  • 1997: PhD (Engineering), Department of Applied Physics, School of Engineering, The University of Tokyo
  • 1997: Research Fellowship, Japan Society for the Promotion of Science
  • 2000: Research Associate, Research Institute for Mathematical Sciences, Kyoto University
Address Research Institute for Mathematical Sciences
Kyoto University, Kyoto 606-8502 Japan
FAX: +81-75-753-7272
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Research Numerical Analysis
Numerical Integration / Quadrature
Hobby Design of electric circuit
My cat
my cat
Papers
T. Ooura and M. Mori, The double exponential formula for oscillatory functions over the half infinite interval, J.Comput. Appl. Math. 38, (1991), 353-360.
M. Mori and T. Ooura, Double exponential formulas for Fourier type integrals with a divergent integrand, Contributions in Numerical Mathematics, ed. R. P. Agarwal, World Scientific Series in Applicable Analysis, 2, (1993), 301-308.
T. Ooura and M. Mori, A robust double exponential formula for Fourier type integrals, J. Comput. Appl. Math., 112, (1999), 229-241.
---- This algorithm is implemented in Mathematica [Mathematica NIntegrate documentation](2008). ----
T. Ooura, A continuous Euler transformation and its application to Fourier transforms of slowly decaying functions (in Japanese), Transactions - Japan Society for Industrial and Applied Mathematics, Vol.9 No.3, (1999), 109-121.
---- Paper prize awarded by JSIAM (2000). ----
T. Ooura, Improvement of the PI Calculation Algorithm and Implementation of Fast Multiple-Precision Computation (in Japanese), Transactions - Japan Society for Industrial and Applied Mathematics, Vol.9 No.4, (1999), 165-172.
---- Paper prize awarded by JSIAM (2001). ----
T. Ooura, Numerical inversion of the Laplace transform using a continuous Euler transformation, RIMS Kokyuroku, Kyoto Univ., (Proceedings), 1145, (2000), 188-193, [pdf 114KB], (Sample c codes [zip 12KB]).
T. Ooura, A continuous Euler transformation and its application to the Fourier transform of a slowly decaying function, J. Comput. Appl. Math., 130, (2001), 259-270.
K. Amano, M. Asaduzzaman, T. Ooura and S. Saitoh, Representation of analytic functions on typical domains in terms of local values and truncation error estimates, Analytic Extension Formulas and their Applications, ed. S. Saitoh, N. Hayashi and M. Yamamoto, Kluwer Academic Publisher (2001), 15-25.
T. Ooura, An Improved Convergence Test for the Double Exponential Formula (in Japanese), Transactions - Japan Society for Industrial and Applied Mathematics, Vol.13 No.2, (2003), 225-230.
---- Paper prize awarded by JSIAM (2005). ----
T. Ooura, A generalization of the continuous Euler transformation and its application to numerical quadrature, J. Comput. Appl. Math., 157, (2003), 251-259.
T. Ooura, A double exponential formula for the Fourier transforms, Publ. RIMS, Kyoto Univ., 41, (2005), 971-978, [pdf], [pdf 164KB], (Sample c code for Approximation Formula 2 [c 4KB]).
T. Ooura, An IMT-type quadrature formula with the same asymptotic performance as the DE formula, J. Comput. Appl. Math., 213, (2008), 232-239.
T. Ooura, A Computation Method for Integral Transforms using the Double Exponential Transformation (in Japanese), Transactions - Japan Society for Industrial and Applied Mathematics, Vol.19 No.1, (2009), 73-79.
M. Shoji, H. Okamoto and T. Ooura, Particle trajectories around a running cylinder or a sphere, Fluid Dynamics Research, 42, (2010), 025506.
T. Ooura, Direct computation of generalized functions by continuous Euler transformation, Sugaku Expositions, 25, (June 2012), 89-104.
T. Ooura, High-speed high-accuracy computation of an infinite integral with unbounded and oscillated integrand, RIMS Preprint, 1741, [pdf], (Sample c code[c 1MB]).
T. Ooura, Fast computation of Goursat's infinite integral with very high accuracy, J. Comput. Appl. Math., 249, (2013), 1-8.
Talks
T. Ooura, Double exponential formula for Fourier type integral, the Sixth International Congress on Computational and Applied Mathematics, Katholieke Universiteit Leuven, (Invited), 1994/7/26-29.
T. Ooura, Continuous Euler transformation and its application to the Fourier transform, The Fifth China-Japan Joint Seminar On Numerical Mathematics, Shanghai Jiao-Tong Univ., 2000/8/23.
T. Ooura, A double exponential formula for the Fourier transforms, Workshop - Thirty Years of the Double Exponential Transforms, Research Institute for Mathematical Sciences, Kyoto University, (Invited), 2004/9/3.
T. Ooura, An IMT-type quadrature formula with the same asymptotic performance as the DE formula, Workshop - Mathematical Sciences for Large Scale Numerical Simulations, Research Institute for Mathematical Sciences, Kyoto University, 2006/11/27.
T. Ooura, Double exponential quadrature for oscillatory integrals, The Third China-Japan-Korea Joint Conference on Numerical Mathematics, Gangneung-Wonju National University, (Invited), 2010/8/23.
T. Ooura, Computation of an infinite integral with unbounded integrand, The 8th International Congress on Industrial and Applied Mathematics, China National Convention Center inside the Beijing Olympic Green, 2015/8/13.
T. Ooura, Double exponential quadratures for various kinds of integral, Second International ACCA-JP/UK Workshop, Kyoto University, 2016/1/19.
Links