
Accession Number : AD0695818
Title : ON THE CONSTRUCTION OF GAUSSIAN QUADRATURE RULES FROM MODIFIED MOMENTS,
Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF COMPUTER SCIENCES
Personal Author(s) : Gautschi,Walter
Report Date : OCT 1969
Pagination or Media Count : 27
Abstract : Given a weight function omega(x) on (alpha, beta), and a system of polynomials (p sub k)(x), k = 0 to infinity, with degree p sub k (x) = k, we consider the problem of constructing Gaussian quadrature rules from 'modified moments'. Classical procedures take p sub k (x) = x, but suffer from progressive illconditioning as n increases. A more recent procedure, due to Sack and Donovan, takes for p sub k (x) a system of (classical) orthogonal polynomials. The problem is then remarkably wellconditioned, at least for finite intervals (alpha, beta). In support of this observation, we obtain upper bounds for the respective asymptotic condition number. In special cases, these bounds grow like a fixed power of n. We also derive an algorithm for solving the problem considered which generalizes one due to Golub and Welsch. Finally, some numerical examples are presented.
Descriptors : (*NUMERICAL ANALYSIS, THEORY), COMPUTER PROGRAMMING, FOURIER ANALYSIS, POLYNOMIALS, ALGORITHMS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE