Some Remarks Concerning Iterative Methods for Linear Systems
Fred B. Weissler · SIAM Journal on Matrix Analysis and Applications · 1995
Let A be a Hermitian, positive definite matrix. It is well known that if $A = M - N$, where M is invertible and $M^ * + N$ is also positive definite, then the iterative method for solving $Au = b$, based on this decomposition, is convergent. A new proof of this convergence is given, providing an explicit estimate for the spectral radius of $M^{ - 1} N$. Also, a new method to estimate the optimal relaxation parameter for certain large matrices is suggested.