×

Error estimates with explicit constants for the sinc approximation over infinite intervals. (English) Zbl 1426.65015

Summary: The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals. Recently, for verified numerical computations, a more explicit, “computable” error bound has been given in the case of a finite interval. In this paper, such explicit error bounds are derived for other cases.

MSC:

65D05 Numerical interpolation
41A30 Approximation by other special function classes
65D15 Algorithms for approximation of functions

Software:

Sinc-Pack
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Stenger, F., Optimal convergence of minimum norm approximations in \(H_p\), Numerische Mathematik, 29, 345-362 (1978) · Zbl 0437.41030
[2] Sugihara, M., Near optimality of the Sinc approximation, Math. Comput., 72, 767-786 (2003) · Zbl 1013.41009
[3] Stenger, F., Numerical Methods Based on Sinc and Analytic Functions (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0803.65141
[4] Stenger, F., Summary of Sinc numerical methods, J. Comput. Appl. Math., 121, 379-420 (2000) · Zbl 0964.65010
[5] Lund, J.; Bowers, K. L., Sinc Methods for Quadrature and Differential Equations (1992), SIAM: SIAM Philadelphia, PA · Zbl 0753.65081
[6] Sugihara, M.; Matsuo, T., Recent developments of the Sinc numerical methods, J. Comput. Appl. Math., 164-165, 673-689 (2004) · Zbl 1038.65071
[7] Mori, M.; Sugihara, M., The double-exponential transformation in numerical analysis, J. Comput. Appl. Math., 127, 287-296 (2001) · Zbl 0971.65015
[8] Tanaka, K.; Sugihara, M.; Murota, K., Function classes for successful DE-Sinc approximations, Math. Comput., 78, 1553-1571 (2009) · Zbl 1198.65037
[9] Takahasi, H.; Mori, M., Double exponential formulas for numerical integration, Publ. Res. Inst. Math. Sci. Kyoto Univ., 9, 721-741 (1974) · Zbl 0293.65011
[10] Muhammad, M.; Mori, M., Double exponential formulas for numerical indefinite integration, J. Comput. Appl. Math., 161, 431-448 (2003) · Zbl 1038.65018
[11] Okayama, T.; Matsuo, T.; Sugihara, M., Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration, Numerische Mathematik, 124, 361-394 (2013) · Zbl 1281.65020
[12] Okayama, T., Error estimates with explicit constants for Sinc quadrature and Sinc indefinite integration over infinite intervals, Rel. Comput., 19, 45-65 (2013)
[13] Okayama, T.; Tanaka, K.; Matsuo, T.; Sugihara, M., 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, 125, 511-543 (2013) · Zbl 1382.65067
[14] Stenger, F., Handbook of Sinc Numerical Methods (2011), CRC Press: CRC Press Boca Raton, FL · Zbl 1208.65143
[15] Okayama, T., A note on the Sinc approximation with boundary treatment, JSIAM Lett., 5, 1-4 (2013) · Zbl 1416.65233
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.