Preconditioned USSOR Iterative Method for H-matrix Linear Systems

When solving linear equations, it is often encountered that the coefficient matrix is an H-matrix. In practical calculations, we often use iterative methods to solve linear equations. To accelerate the convergence speed of iterative methods, we usually use preprocessing techniques to solve linear equations. In this article, the preconditioner \(P_{\xi } = I + S_{\xi }\) is presented. Under certain conditions, the convergence of the preconditioned USSOR iterative method for H-matrix linear systems is proved. Finally, a numerical example for corresponding preconditioned USSOR iterative method is also given to illustrate the conclusion.