A class of accelerated parameterized inexact Uzawa algorithms for complex symmetric linear systems

摘要

We establish a class of accelerated parameterized inexact Uzawa (APIU) algorithms for solving the complex symmetric linear systems. Our main contribution is accelerating the convergence of the PIU algorithm by making use of the extrapolation technique which is based on the eigenvalues of the iterative matrix. These accelerated parameterized inexact Uzawa algorithms involve two iteration parameters whose special choices can recover the parameterized inexact Uzawa algorithm and some other methods. First, the accelerated model for the PIU algorithm is established and the accelerated PIU algorithm is presented. Then we study the convergence of the corrected PIU algorithm. Moreover, we present the optimal iteration parameter and the corresponding optimal convergence factor for the PIU method. We also consider acceleration of the PIU iteraton by Krylov subspace methods. Numerical experiments are presented to illustrate the theoretical results and examine the numerical effectiveness of the new method.