On Mixed Precision Iterative Refinement for Eigenvalue Problems

摘要

We investigate novel iterative refinement methods for solving eigenvalue problems which are derived from Newton's method. In particular, approaches for the solution of the resulting linear system based on saddle point problems are compared and evaluated. The algorithms presented exploit the performance benefits of mixed precision, where the majority of operations are performed at a lower working precision and only critical steps within the algorithm are computed in a higher target precision, leading to a solution which is accurate to the target precision. A complexity analysis shows that the best novel method presented requires fewer floating point operations than the so far only existing iterative refinement eigensolver by Dongarra, Moler and Wilkinson.