Use of the Singular Value Decomposition with the Manteuffel Algorithm for Nonsymmetric Linear Systems
Paul E. Saylor · SIAM Journal on Scientific and Statistical Computing · 1980
Optimum Chebyshev parameters may be computed dynamically by the Manteuffel algorithm for use with a generalization of Richardson’s iterative method and the Jacobi semi-iterative method to solve nonsymmetric linear algebraic systems. The algorithm determines the convex hull of eigenvalues of a matrix associated with the system and from the convex hull determines the parameters. The singular value decomposition may be used to test the reliability of a simple technique to reduce execution and storage costs of the power method. The same technique also yields an inexpensive singular value decomposition, making it feasible to determine precisely when to call the Manteuffel algorithm.