Several Preconditioned Tensor Splitting Iterative Methods For Solving Multi-linear Systems

Many problems in engineering and scientific computing involve the solution of multi-linear systems,such as tensor complementarity problems,numerical partial differential equations,evolutionary game dynamics,data mining and so on.Hence,solving multi-linear systems has become a hot topic.In order to improve the approximate convergence and reduce the calculation cost,scholars have proposed to use tensor splitting iterative method to solve multi-linear systems.On the basis of preconditioned techniques,this thesis mainly studies the preconditioned tensor splitting iterative method for solving multi-linear systems.First of all,the preconditioned Gauss-Seidel method with the dual-parameter type preconditioner is proposed,the convergence of this method is analyzed,and comparison theorems and numerical examples are given to verify the efficiency of the dual-parameter type preconditioner.Secondly,the preconditioned Gauss-Seidel method with the max-type preconditioner is given,the convergence of this method is investigated,and the efficiency of the max-type preconditioner is shown by some comparative results and numerical examples.Finally,the preconditioned SOR method with the max-parameter type preconditioner is given,the convergence of this method is discussed,and comparison theorems and numerical examples are given to illustrate the efficiency of the max-parameter type preconditioner.