Preconditioned Iterative Method For Solving Multi-linear Systems

With the advent of big data,the multi-liner systems has attracted much attention in the fields of data mining,differential equation and engineering calculation and so on.Particularly,the numerical solution of multi-linear systems is an important part of multi-liner systems.However,it is difficult to solve the multi-liner systems.Therefore,studying the iterative methods of solving multi-liner systems has important theoretical significance and practical application background.The main purpose of this paper is devoted to solving the multi-liner systems by the preconditioned Jacobi iterative methods and the preconditioned Gauss-Seidel iterative methods based on the tensor splittings.Firstly,we consider a new preconditioner I+G?,which is constructed by the elements at first column of the majorization matrix of A,and propose the preconditioned Jacobi type iterative tensors and Gauss-Seidel type iterative tensors according to the different tensor splittings,and prove the proposed tensor splittings are converged.Secondly,we give spectral radius comparisons of the different preconditioned iterative tensors.In particular,also we prove that ?(B?'")is monotonically decreasing function of any parameter ?i.Finally,numerical results are reported to show that the efficiency of the proposed splitting iterative methods.