Numerical stability of iterative refinement with a relaxation for linear systems
Provides theoretical stability analysis for a variant of iterative refinement, but the result is incremental as it confirms the existing choice omega=1 is optimal.
The paper analyzes the numerical stability of iterative refinement with relaxation (IR(omega)) for solving linear systems, extending existing results for omega=1. Numerical tests confirm that omega=1 is the best choice for stability.
Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson's iterative refinement. We assume that all computations are performed in fixed (working) precision arithmetic. Numerical tests were done in MATLAB to illustrate our theoretical results. A particular emphasis is given on convergence of iterative refinement with a relaxation. Our tests confirm that the choice omega=1 is the best choice from the point of numerical stability.