Uniform approximations to finite Hilbert transform and its derivative

Journal of Computational and Applied Mathematics

Volumn 163, Issue 1, 2004, Pages 127-138

  Hasegawa, Takemitsu ^a  

^a UNIVERSITY OF FUKUI   (Japan)

Author keywords

Cauchy principal value integrals; Error analysis; Hadamard finite part integrals; Qaudrature rules

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INTEGRATION; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS;

HILBERT TRANSFORM;

APPROXIMATION THEORY;

MATHEMATICAL METHOD;

EID: 1642521646     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.08.059     Document Type: Article

References (21)

1. Bialecki B. A Sinc quadrature rule for Hadamard finite-part integrals Numer. Math. 57 1990 263-269
2. Criscuolo G. A new algorithm for Cauchy principal value and Hadamard finite-part integrals J. Comput. Appl. Math. 78 1997 255-275
3. Criscuolo G. Scuderi L. The numerical evaluation of Cauchy principal value integrals with non-standard weight functions BIT 38 1998 256-274
4. Davis P.J. Rabinowitz P. Methods of Numerical Integration 2nd Edition 1984 Academic Press Orland, FL
5. Diethelm K. Generalized compound quadrature formulae for finite-part integrals IMA J. Numer. Anal. 17 1997 479-493
6. Diethelm K. A method for the practical evaluation of the Hilbert transform on the real line J. Comput. Appl. Math. 112 1999 45-53
7. Elliott D. Truncation errors in two Chebyshev series approximations Math. Comput. 19 1965 234-248
8. Elliott D. Three algorithms for Hadamard finite-part integrals and fractional derivatives J. Comput. Appl. Math. 62 1995 267-283
9. Elliott D. Venturino E. Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals Numer. Math. 77 1997 453-465
10. Gautschi W. Varga R.S. Error bounds for Gaussian quadrature of analytic functions SIAM J. Numer. Anal. 20 1983 1170-1186
11. Gentleman W.M. Implementing Clenshaw-Curtis quadrature II: computing the cosine transformation Comm. ACM 15 1972 343-346
12. Hasegawa T. Torii T. An automatic quadrature for Cauchy principal value integrals Math. Comput. 56 1991 741-754
13. Hasegawa T. Torii T. Hilbert and Hadamard transforms by generalized Chebyshev expansion J. Comput. Appl. Math. 51 1994 71-83
14. Hasegawa T. Torii T. Ninomiya I. Generalized Chebyshev interpolation and its application to automatic quadrature Math. Comput. 41 1983 537-553
15. Hasegawa T. Torii T. Sugiura H. An algorithm based on the FFT for a generalized Chebyshev interpolation Math. Comput. 54 1990 195-210
16. Kumar S. A note on quadrature formulae for Cauchy principal value integrals J. Inst. Math. Appl. 26 1980 447-451
17. Linz P. On the approximate computation of certain strongly singular integrals Computing 35 1985 345-353
18. Monegate G. Numerical evaluation of hypersingular integrals J. Comput. Appl. Math. 50 1994 9-31
19. Monegate G. Lyness J.N. The Euler-Maclaurin expansion and finite-part integrals Numer. Math. 81 1998 273-291
20. Paget D.F. The numerical evaluation of Hadamard finite-part integrals Numer. Math. 36 1981 447-453
21. Rivlin T.J. Chebyshev Polynomials, From Approximation Theory to Algebra and Number Theory 2nd Edition 1990 Wiley New York