# Iterative Solutions of Systems of Linear Equations Whose Coefficient Matrix Is Positive Real

## Document Type

Article

## Department

Mathematics (HMC)

## Publication Date

7-1986

## Abstract

During the academic year 1981-82, we worked, together with a team of students and faculty under the auspices of the Claremont Mathematics Clinic, on a problem in computational aerodynamics that resulted in the report [L]. The problem came from an engineering group at Lockheed-California, who were modeling the flow of air over the surface of an aircraft. They obtained large full systems of linear equations of the form *A*x = *b*, where *A *is a matrix with real entries such that x* ^{t}A*x>0 for all nonzero real vectors x, and were applying a version of successive over-relaxation (SOR). Such a matrix is called

*positive real*in [Y] and can have complex eigenvalues, hence need not be similar to a (symmetric) positive definite matrix. Below we give some intervals of ∞-values for which the SOR iteration matrix

*L*(

_{w}*A*) has spectral radius less than 1, when

*A*is positive real and satisfies other conditions. We supply a few pertinent examples and discuss the necessity of some of these conditions.

## Rights Information

© 1986 Gordon and Breach Science Publishers

## DOI

10.1080/03081088608817721

## Recommended Citation

Day, Jane M. and Melvin Henriksen. 1986. Iterative solutions of systems of linear equations whose coefficient matrix is positive real. Linear and Multilinear Algebra. 19(3):267-285.