MA60: Iterative refinement and error estimation

This subroutine performs iterative refinement and provides information on the error in the resulting solution of a set of \(n\) sparse linear equations \(\bf A \bf x = \bf b\), either as an upper bound on the actual error (forward error) or as a bound on the perturbation to the matrix elements which would make the solution obtained the exact solution of a perturbed problem with the same sparsity pattern as the original matrix (backward error). All estimates are provided in the \(\infty\)-norm, that is \(|| \mathbf {x} || _\infty = \max _ i | x _i |\).

There is an option for avoiding iterative refinement, in which case bounds on the errors associated with the given solution are provided.