Synchronous Multisplitting Iterative Methods For Relaxed Modular Systems For A Class Of Nonlinear Complementary Problems

This thesis focuses on a class of nonlinear complementarity problems.On the basis of the existing research results,two kinds of general relaxation modulus-based synchronous multisplitting iterative methods are investigated,and the proposed methods rely on the known modulus-based matrix splitting iterative methods.Specifically,the nonlinear complementarity problem is first equivalently transformed into an implicit fixed-point equation.Then,the convergence is discussed when the system matrix is ?+-matrix.The nonlinear terms are handled skillfully,the convergence analysis are given.Finally,the validity of the proposed methods is verified by numerical experiments.The new methods are efficient in terms of iteration steps and CPU times.The contributions of this thesis include:(1)Based on the modulus-based synchronous multisplitting iterative methods for a restricted class of nonlinear complementarity problems presented by Wu Yujiang et al.on Numer.Math.Theory Methods Appl.in 2019,and the general modulus-based equations of nonlinear complementarity problems,the general external relaxation modulus-based synchronous multisplitting iterative method is established.Theoretical analysis and numerical experiments are implemented,which show the efficiency of the proposed method.(2)By introducing a positive diagonal parameter matrix to mix the new approach vector and the old approach vector before the next iterative,the general internal relaxation modulus-based synchronous multisplitting iterative method is presented.Theoretical analysis and numerical experiments are carried out to prove the efficiency of the proposed method.