Generalization of Interval Jacobi and Gauss-Seidel Methods for Interval Linear System

Abstract

The paper presents iterative methods for solving interval linear system of equations. We present a generalization of interval Jacobi method and interval Gauss-Seidel method by generalizing interval diagonal matrices to band interval matrices, and discuss the convergence analysis of the proposed methods. More specifically, we prove that both the proposed methods converge for any initial approximation if the coefficient interval matrix of the system is either an interval strictly diagonally dominant matrix, or interval M-matrix or interval H-matrix. Numerical experiment are carried out to assess the effectiveness of the proposed methods.