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 ill-conditioning 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 well-conditioned, 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