The Research On Numerical Algorithms For Large-scale Stein Equations Based On Krylov Subspace

Solving large matrix equations has always been the focus of numerical computation research,and has been widely used in simulation prediction,dynamic systems,image processing,etc.The Krylov subspace method,as one of the main methods to deal with such problems,shows that its unique superiority and huge potential.This dissertation is mainly aimed at large-scale Stein equations.Based on the existing methods,a suitable global Arnoldi process is developed,and a global full orthogonal method(GL-FOM)and a global generalized minimum residual method(GL-GMRES)are proposed.With the increase in computational cost,on this basis,we propose a restart version of these two algorithms.In order to accelerate convergence,the weighted strategy is also a widely known way.We compare with previous conclusions and analyze the inherent relationship between the orthogonal matrices obtained from the theoretically weighted and unweighted strategies and the corresponding residuals,which shows that the global approach is a special form of weighted strategy,and we propose a new way to choose weight factors.Finally,numerical experiments prove the feasibility of the algorithms with numerical performance.