Accession Number : AD0608854

Title :   NUMERICAL CONTOUR INTEGRATION.

Descriptive Note : Doctoral thesis,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Barnhill,Robert Ellis

Report Date : OCT 1964

Pagination or Media Count : 86

Abstract : This paper is concerned with numerical integration along contours in the complex plane. Let R sub n denote the quadrature remainder with n evaluation points. An error functional related to R sub n is minimized, subject to the constraint that R sub n (f) be exact whenever f is a polynomial of certain degree. A special case is given, with computed examples of the theory's application. Another problem considered is that of the convergence of quadratures as the number of evaluation points increases. Theorems characterizing the domains of holomorphy that ensure convergence are given. (Author)

Descriptors :   (*COMPLEX VARIABLES, FUNCTIONS(MATHEMATICS)), (*NUMERICAL INTEGRATION, COMPLEX VARIABLES), (*NUMERICAL ANALYSIS, NUMERICAL INTEGRATION), INTEGRALS, POLYNOMIALS

Distribution Statement : APPROVED FOR PUBLIC RELEASE