| The generalized absolute value equations(GAVE)arise in various areas of scientific computations and engineering applications,and how to improve the efficiency of the solving methods is an important research topic.In this thesis,three efficient splitting iteration algorithms are proposed.The convergence analyses of the proposed algorithms are discussed,and the numerical effectiveness is examined through numerical experiments.The thesis is organized as follows:In Chapter 1,we describe the research background and research status of the GAVE,and introduce the related preliminary knowledge and some useful lemmas.In Chapter 2,we propose the shift splitting fixed point iteration(FPI-SS)method for solving generalized absolute value equation,the convergence theorems are presented,and two numerical examples from the linear complementarity problems(LCP)are reported to illustrate the effectiveness of the FPI-SS method.In Chapter 3,we introduce the matrix splitting fixed point iteration(FPI-MS)method which includes the FPI-SS method as a special case.The convergence conditions and the theoretical quasi-optimal parameters are discussed.Finally,numerical experiments show the feasibility and efficiency of this iteration method.In Chapter 4,using matrix splitting iteration method,the matrix splitting new SOR-like(NSOR-MS)iteration method for solving GAVE is established.We discuss the convergence conditions of this iteration method.Finally,the NSOR-MS iteration method is shown to be an efficient iteration method through numerical experiments.In Chapter 5,we give the conclusions of this thesis and some future works. |
