‖A‖_m≥1的Gauss－Seidel迭代法收敛的新判据

Criteria for Convergence of the Gauss-Seidel Iteration in Which it‖A‖_m≥1

本文给出了当时，Ｇａｕｓｓ－ｓｅｉｄｅｌ迭代法收敛的充分条件，将收敛的限制由‖Ａ‖＜１扩充到‖Ａ‖ｍ＞１上，该判据易于检验，适用范围广。

Abstract In this paper,some new criteria for convergence of the Gauss-Seidel iteration are presented. We can extent the limitation of the convergence of the Gauss-Seidel iteration from ‖A‖i< 1,‖A‖∞<1to‖A‖m≥1 in some extent.