A sharp error bound of the approximate solutions for saddle point linear systems

Sharp error estimations for numerical solutions of saddle point linear systems are presented. Based on these estimations, fast algorithms for computing error bounds of the numerical solutions are proposed. The error bounds obtained by these algorithms are “verified” in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the computation and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms.