ITERATIVE REFINEMENT FOR LINEAR-SYSTEMS AND LAPACK

The technique of iterative refinement for improving the computed solut ion to a linear system was used on desk calculators and computers in t he 1940s and has remained popular. In the 1990s iterative refinement i s well,supported in software libraries, notably in LAPACK. Although th e behaviour of iterative refinement in floating point arithmetic is re asonably well understood, the existing theory is not sufficient to jus tify the use of fixed precision iterative refinement in all the LAPACK routines in which it is implemented. We present analysis that provide s the theoretical support needed for LAPACK. The analysis covers both mixed and fixed precision iterative refinement with an arbitrary numbe r of iterations, makes only a general assumption on the underlying sol ver, and is relatively short. We identify some remaining open problems .