Subtracting out complex singularities in numerical integration
Author:
F. G. Lether
Journal:
Math. Comp. 31 (1977), 223-229
MSC:
Primary 65D30
DOI:
https://doi.org/10.1090/S0025-5718-1977-0423768-2
MathSciNet review:
0423768
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: This paper is concerned with the numerical approximation of definite integrals over , in which the function f to be integrated has isolated singularities near
. Complex variable techniques are used to study the effectiveness of the method of subtracting out complex singularities.
- [1] L. V. KANTOROVITCH, "On approximate calculation of certain types of definite integrals and other applications of the method of selection of the singularities," Mat. Sb., v. 41, 1934, pp. 235-245.
- [2] V. I. KRYLOV, Approximate Calculation of Integrals, Fizmatgiz, Moscow, 1959; Transl, by A. H. Stroud, Macmillan, New York, 1962. MR 22 #2002; 26 #2008. MR 0144464 (26:2008)
- [3] J. McNAMEE, "Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae," Math. Comp., v. 18, 1964, pp. 368-381. MR 32 #3264. MR 0185804 (32:3264)
- [4] W. E. SMITH & J. N. LYNESS, "Applications of Hilbert transform theory to numerical quadrature," Math. Comp., v. 23, 1969, pp. 231-252. MR 40 #5132. MR 0251906 (40:5132)
- [5] F. STENGER, "Bounds on the error of Gauss-type quadratures," Numer. Math., v. 8, 1966, pp. 150-160. MR 33 #5120. MR 0196936 (33:5120)
- [6] G. SZEGÖ, Orthogonal Polynomials, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 21 #5029. MR 0106295 (21:5029)
Retrieve articles in Mathematics of Computation with MSC: 65D30
Retrieve articles in all journals with MSC: 65D30
Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1977-0423768-2
Keywords:
Complex singularities,
quadrature,
subtracting out singularities
Article copyright:
© Copyright 1977
American Mathematical Society