Accession Number : ADA309671

Title :   Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators.

Descriptive Note : Research rept.,

Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE

Personal Author(s) : Rokhlin, Vladimir ; Yarvin, Norman

PDF Url : ADA309671

Report Date : MAY 1996

Pagination or Media Count : 44

Abstract : Generalized Gaussian quadratures appear to have been introduced by Markov late in the last century, and have been studied in great detail as a part of modern analysis. They have not been widely used as a computational tool, in part due to absence of effective numerical schemes for their construction. Recently, a numerical scheme was introduced for the design of such quadratures; numerical results presented indicate that such quadratures dramatically reduce the computational cost of the evaluation of integrals under certain conditions. In this paper, we modify the approach, improving the stability of the scheme and extending its range of applicability. The performance of the method is illustrated with several numerical examples.

Descriptors :   *ALGORITHMS, *GAUSSIAN QUADRATURE, MATRICES(MATHEMATICS), ACCURACY, MATHEMATICAL PROGRAMMING, APPROXIMATION(MATHEMATICS), NUMERICAL INTEGRATION, INTERPOLATION, CONVERGENCE, SYSTEMS ANALYSIS, OPERATORS(MATHEMATICS), EXPONENTIAL FUNCTIONS, INTEGRAL TRANSFORMS, BESSEL FUNCTIONS, LEGENDRE FUNCTIONS, NUMERICAL QUADRATURE, CHEBYSHEV POLYNOMIALS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE