New techniques for the solution of linear systems by iterative methods (Q1094091)

A new iteration method is introduced for solving linear equations \(Ax=b\) on the basis of splitting \(A=(A-M)+M\), where \(M^{-1}\) is a symmetric tridiagonal matrix, and the Frobenius norm of the iteration matrix is minimized. Numerical examples are provided, showing that the algorithm improves the rate of convergence of the Jacobi method without increasing the order of magnitude of the computational effort required.