A geometric approach for computing a posteriori error bounds for the solution of a linear system (Q1179535)

The author describes a geometric approach to the computation of a posteriori error bounds for the solution of a linear system. Given the linear system \(Ax=b\) with computed solution \(\bar x\) and an approximation \(R\) to \(A^{-1}\) he uses \(R\) to compute a guaranteed error bound for \(\bar x\). As an example the case of a small well-conditioned system is considered. The author also formulates some remarks on the case of ill-conditioned systems, in particular on systems with a Hilbert matrix.