Subtracting out complex singularities in numerical integration
HTML articles powered by AMS MathViewer
- by F. G. Lether PDF
- Math. Comp. 31 (1977), 223-229 Request permission
Abstract:
This paper is concerned with the numerical approximation of definite integrals over $[ - 1,1]$, in which the function f to be integrated has isolated singularities near $[ - 1,1]$. Complex variable techniques are used to study the effectiveness of the method of subtracting out complex singularities.References
-
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.
- Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Company, New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR 0144464
- John McNamee, Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp. 18 (1964), 368–381. MR 185804, DOI 10.1090/S0025-5718-1964-0185804-1
- W. E. Smith and J. N. Lyness, Applications of Hilbert transform theory to numerical quadrature, Math. Comp. 23 (1969), 231–252. MR 251906, DOI 10.1090/S0025-5718-1969-0251906-9
- Frank Stenger, Bounds on the error of Gauss-type quadratures, Numer. Math. 8 (1966), 150–160. MR 196936, DOI 10.1007/BF02163184
- Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 223-229
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1977-0423768-2
- MathSciNet review: 0423768