Term of Award

Spring 1997

Degree Name

Master of Science in Mathematics

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematics

Committee Chair

Xiezhang Li

Committee Member 1

Lila Roberts

Committee Member 2

Richard J. Hathaway

Abstract

The Chebyshev semi-iterative method, CHSIM, is probably the most often used to solve iteratively linear systems x=Mx+g, where the only requirement on the matrix M is that it be Hermitian. However, a knowledge of bounds a and b for the largest and smallest eigenvalues of the matrix is required. This thesis presents a procedure for using the CHSIM without knowledge of a or b. The procedure uses variations in the convergence factor, produced by the use of the CHSIM with approximated values of the bounds a and b, to find better approximations for these bounds. Different cases are studied and numerical results are reported.

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