Abstract: The Richardson iterative method was extended to solve more general linear equations. First, the iterative process and the iterative matrix were reformulated by using the similar transformation matrix, based on minimizing spectral radius of the iterative matrix, and the method of selecting the optimal relaxation parameter was given. Then aiming at the problem that the smallest eigenvalue was difficult to calculate, an accelerated convergence strategy was proposed, which only depended on the largest eigenvalue.

Key words: iterative algorithm, relaxation parameter, iterative , matrix, spectral radius