Iterative refinement techniques for solving block linear systems of equations

We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations A x = b with A partitioned into blocks using floating point arithmetic. We assume that all computations are performed in the working (fixed) precision. We prove that the numerical quality of RIR is superior to that of IR.