Applying the Chebyshev Semi-Iterative Method When the Bounds of the Eigenvalues Are Unknown

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