Near optimality of the sinc approximation

Mathematics of Computation

Volumn 72, Issue 242, 2003, Pages 767-786

  Sugihara, Masaaki ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Double exponential formula; Near optimality; Sinc approximation; Variable transformation

Indexed keywords

EID: 0037378162     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-02-01451-5     Document Type: Article

References (21)

1. M. Abramowitz and I. Stegun, Handbook of mathematical functions, NBS Applied Math. Series 53, 1964. MR 29:4914
2. p functions, Math. Z. 172 (1980), 55-62. MR 83m:41023
3. p par des polynômes de degrées très élevés, Bull. Acad. Sci. USSR, Cl. Sci. Math. Nat. 2 (1938), 181-190.
4. q(-1,1), SIAM J. Math. Anal. 16 (1985), 405-421. MR 86i:41021
5. μ, in: Quantitative Approximation (R. A. DeVore and K. Scherer, eds.), Academic Press, London, 1980, 121-132. MR 81m:41008
6. T. H. Ganelius, Rational approximation in the complex plane and on the line, Ann. Acad. Sci. Fenn. Ser. A.I. 2 (1976), 129-145. MR 58:17106
7. α, in: Computation and Control II(K. L. Bowers and J. Lund, eds.), Birkhäuser, Basel, 1991, 161-171. MR 92g:93006
8. β by sinc functions, J. Approx. Th. 66 (1991), 44-52. MR 92d:41047
9. M. A. Kowalski, K. A. Sikorski, and F. Stenger, Selected topics in approximation and computation, Oxford Univ. Press, Oxford, 1995. MR 97k:41001
10. J. Lund and K. L. Bowers, Sinc methods for quadrature and differential equations, SIAM, Philadelphia, PA, 1992. MR 93i:65004
11. M. Mori and M. Sugihara, The double exponential transformation in numerical analysis, in: Numerical Analysis in the 20th Century Vol. V: Quadrature and Orthogonal Polynomials, J. Comput. Appl. Math. 127 (2001), 287-296. MR 2001k:65041
12. p functions, Math. Z. 166 (1979), 111-115. MR 80g:41022
13. J. R. Rice, On the degree of convergence of nonlinear spline approximation, in: Approximations with Special Emphasis on Spline Functions (I. J. Schoenberg, ed.), Academic Press, New York, 1969, 349-365. MR 42:2226
14. p, Numer. Math. 29 (1978), 345-362. MR 58:3342
15. F. Stenger, Numerical methods based on Whittaker cardinal or sinc functions, SIAM Rev. 23 (1981), 165-224. MR 83g:65027
16. F. Stenger, Explicit nearly optimal linear rational approximation with preassigned poles, Math. Comput. 47 (1986), 225-252. MR 87g:41034
17. F. Stenger, Numerical methods based on sinc and analytic functions, Springer-Verlag, New York, 1993, MR 94k:65003
18. F. Stenger, Summary of sinc numerical methods, in: Numerical Analysis in the 20th Century Vol. I: Approximation Theory, J. Comput. Appl. Math. 121 (2000), 379-420. MR 2001d:65018
19. M. Sugihara, Optimality of the double exponential formula - functional analysis approach, Numer. Math. 75 (1997), 379-395. MR 97i:41041
20. H. Takahasi and M. Mori, Double exponential formulas for numerical integration, Publ. RIMS Kyoto Univ. 9 (1974), 721-741. MR 49:11781
21. q(-1,1), J. Complexity 8 (1992), 324-335. MR 94e:46051