On the Determination of the Optimum Relaxation Factor for the SOR Method When the Eigenvalues of the Jacobi Method are Complex.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1970
- Accession Number
- AD0715001
Entities
People
- David M. Young
- Harold D. Eidson
Organizations
- University of Texas at Austin