CHAPTER 5 - An Adaptive Chebyshev Procedure Using Special Norms

Abstract

This chapter presents parameter estimation and stopping procedures for the Chebyshev acceleration method applied to the basic iterative process. The basic method is symmetrizable. In the adaptive procedure, a test is made during each iteration to determine whether the acceleration parameters are satisfactory. If the acceleration parameters are judged unsatisfactory, the adaptive procedure then gives new estimates for the required parameters. The decisions made by the adaptive procedure are based on a comparison of the observed error reduction of the iterates with the expected error reduction when the estimated parameters are optimal. To obtain the optimum Chebyshev parameters, both m(G) and M(G) must be known. Pseudoresidual vector plays an important role in the adaptive procedure. This chapter discusses the use of the adaptive procedure, utilizing the W-norm when the basic method is either the Jacobi method or the symmetric successive overrelaxation method.