Research On Iterative Algorithm For Solving Nonsingular M-tensor Equation

The M-tensor equation in the numerical solution of partial differential equation is of important application value.Based on the tensor divided technology is put forward to solve the singular M-tensor equation of accelerated over-relaxation method?hereinafter referred to as AOR method?,Numerical experiments show that the AOR method is faster than Jacobi method,Gauss-Seidel method and SOR method in some cases.Based on accelerated over-relaxation iteration method,this paper further research to solve the tensor-equation^1-8)=(7 conditions of accelerated over-relaxation itera-tion method?hereinafter referred to as PAOR method?,theis A nonsingular M-tensor.The main job is to put forward the appropriate conditions,the preliminary conditions accelerated over-relaxation iteration convergence of the algorithm and corresponding to different preconditioned iterative tensor changes of the spectrum.Specific research pro-cess is through the comparison of spectral radius theorems and their proofs are given.It is concluded that the spectral radius of the iterative tensor in PAOR method is smaller than that in AOR method.Finally,the iterative algorithm of accelerated over-relaxation and the iterative algorithm of non-negative tensor spectrum radius designed in this pa-per are used,and the iterative algorithm of preconditioned accelerated over-relaxation is proposed.