An optimum iterative method for solving any linear system with a square matrix
A method is presented to solve Ax=b by computing optimum iteration parameters for Richardson's method. It requires some information on the location of the eigenvalues of A. The algorithm yields parameters well-suited for matrices for which Chebyshev parameters are not appropriate. It therefore supplements the Manteuffel algorithm, developed for the Chebyshev case. Numerical examples are described.
Smolarski, D. C., & Saylor, P. E. (1988). An optimum iterative method for solving any linear system with a square matrix. BIT Numerical Mathematics, 28(1), 163–178. https://doi.org/10.1007/BF01934703