The Numerical Method And Perturbation Analysis For Large Sparse Linear System

The numerical method for large sparse linear systems is an important subject inthe field of scientific computing and numerical algebra, and the generalized inversetheory is an important part in large sparse linear systems. In this paper, we focus onstudying the perturbation bounds for generalized singular values and the optimalperturbation bounds of weighted Moore-Penrose inverse by the generalized singularvalues composition, we also improve the perturbation bounds of some linear systemsby the effective condition number. The main research contents are as follows.The first chapter mainly introduces the study background, scientific significanceof the numerical method and perturbation analysis for large sparse linear systems, aswell as the detail of the article.The second chapter mainly introduces the optimal perturbation bounds ofweighted Moore-Penrose inverse under Frobenius norm by the generalized singularvalues composition.The third chapter mainly studys the additive and multiplicative perturbationbounds for generalized singular values compositions, a Hoffman-Wielandt type boundfor generalized singular values under additive perturbation and a Bauer-Fike typebound for generalized singular values under multiplicative perturbation.The fourth chapter mainly studys the eigenvalues properties of constraintpreconditioned linear systems for singular saddle problems and improves theperturbation bounds of preconditioned linear systems by the effective conditionnumber.