Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations (Q1398048)

Let \(Ax= b\) be a system of linear equations with quadratic nonsingular coefficient matrix \(A\), let \(x^*\) be the solution of the system and \(\widetilde x\) be an approximative solution. Then componentwise bounds of the error \(\widetilde x- x^*\) are determined where the residuum \(z= A\widetilde x-b\) and an approximate solution \(\widetilde x\) of the residual equation \(Ax= r\) is utilized. Special attention is payed to the case where \(A\) is symmetric.