Perturbation analysis of saddle-point problems

Abstract

The saddle-point systemis considered, where A is an matrix with full column rank, B is an symmetric and positive definite matrix, and b is an m-vector. When the perturbed systems are still saddle-point systems, perturbation theory is presented under three cases, such as the case of A and b perturbed, the case of B and b perturbed, and the case of A, B and b perturbed. We find that the bounds for the errors of the solution depend on A and B. To remove their influence, some conditions are disposed. To improve the accuracy of the solution, a scaling is given. When the perturbed systems are generalized saddle-point systems, the block factorization is applied. Thus the sensitivity of the block factorization should be discussed, then perturbation theorems for this case are presented.