科研之友
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摘要
The saddle-point system is considered, where A is an m x n matrix with full column rank, B is an m x m 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 LDLT factorization is applied. Thus the sensitivity of the block LDLT factorization should be discussed, then perturbation theorems for this case are presented.
