Accession Number : AD0715001

Title :   On the Determination of the Optimum Relaxation Factor for the SOR Method When the Eigenvalues of the Jacobi Method are Complex.

Descriptive Note : Interim technical rept. no. 26,

Corporate Author : TEXAS UNIV AUSTIN CENTER FOR NUMERICAL ANALYSIS

Personal Author(s) : Young,David M. ; Eidson,Harold D.

Report Date : SEP 1970

Pagination or Media Count : 73

Abstract : Let A be a real consistently ordered matrix with non-vanishing diagonal elements. The eigenvalues lambda of the matrix L sub omega corresponding to the successive over-relaxation method are related to the eigenvalues mu of the matrix B corresponding to the Jacobi method by Lambda + omega mu(squared root of Lambda). If the eigenvalues of B are real, then the optimum value of the relaxation factor omega in the sense of minimizing the spectral radius S(L sub omega) of omega is given by omega sub b = 2/(1+ the squared root of (1-mu bar squared)) where mu bar = S(B). The object of the present paper is to describe a method and a computer program based on this method for determining the optimum value of omega corresponding to a finite set of (complex) values of mu. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), NUMERICAL ANALYSIS), COMPLEX NUMBERS, ITERATIONS, CONVERGENCE, PARTIAL DIFFERENTIAL EQUATIONS, ALGORITHMS, COMPUTER PROGRAMS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE