Iterative Refinement in Three Precisions.
Support for multiprecision floating point arithmetic is increasingly common in emerging architectures. In an effort to exploit this available hardware, we present a general algorithm for solving an n × n nonsingular linear system Ax = b based on iterative refinement in three precisions, where the most expensive part of the computation can be performed in low precision. Our rounding error analysis provides sufficient conditions for convergence and bounds for the attainable normwise forward error and normwise and componentwise backward errors, generalizing and unifying many existing rounding error analyses for iterative refinement. We further investigate the extension of our approach to least squares problems.
