Improved convergence criteria for Jacobi and Gauss–Seidel iterations

摘要

Some simple criteria for the convergence of the Jacobi, Gauss–Seidel and SOR iterations have been proposed in the work of Huang [ZAMM 76-1 (1996) 57–58]. In this study we present some modified forms of the criteria introduced in Huang's work. The new criteria also allow for the norms of the Jacobi iteration matrices to be greater than unity. Numerical examples are also given which show the effectiveness of the criteria.