Numerical indefinite integration by double exponential sinc method
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- by Ken’ichiro Tanaka, Masaaki Sugihara and Kazuo Murota PDF
- Math. Comp. 74 (2005), 655-679 Request permission
Abstract:
We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with $N$ integrand function evaluations is \[ \mathrm {O}(\exp (-c_1 N/\log (c_2 N))) \] for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary sinc method. Computational results show the accordance of the actual convergence rates with the theoretical estimate.References
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Additional Information
- Ken’ichiro Tanaka
- Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
- Email: kenitiro@misojiro.t.u-tokyo.ac.jp
- Masaaki Sugihara
- Affiliation: Department of Computational Science and Engineering, School of Engineering, Nagoya University, Nagoya 464-8603, Japan
- Email: sugihara@na.cse.nagoya-u.ac.jp
- Kazuo Murota
- Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
- Email: murota@mist.i.u-tokyo.ac.jp
- Received by editor(s): May 9, 2003
- Published electronically: November 2, 2004
- Additional Notes: This work is supported by the 21st Century COE Program on Information Science and Technology Strategic Core and a Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 655-679
- MSC (2000): Primary 41A30, 41A25, 65D30
- DOI: https://doi.org/10.1090/S0025-5718-04-01724-7
- MathSciNet review: 2114642