A new parameter-free method for Toeplitz systems of weakly nonlinear equations

摘要

Based on the fact that the linear term is strongly dominant over the nonlinear term, by using the approximate inverse-free preconditioned conjugate gradient (AIPCG) iteration technique, we establish the Picard-AIPCG iteration method to solve Toeplitz systems of weakly nonlinear equations. Since the storage and the accurate computation of Jacobian matrix are not necessary in this method and the only need is to solve the constant Toeplitz sub-systems, there may be a great saving in computer storage and calculation workload when facing the practical problems. The global convergence has been proved under some suitable conditions. Some numerical examples demonstrate the feasibility and effectiveness of this new iteration. (c) 2021 Elsevier B.V. All rights reserved.