Gradient based iterative methods for solving symmetric tensor equations

Abstract The steepest descent and conjugate gradient methods are classical gradient based iterative methods for solving symmetric positive definite linear system . In this article, we are concerned with the numerical solution of the tensor equation by those well‐known iterations in which is an m th order n ‐dimensional symmetric tensor. Then we prove that the developed iterative methods converge locally linearly under some appropriate conditions. Finally, some numerical experiments are provided to illustrate the feasibility and effectiveness of the proposed methods.