An Improved SIRA Method For Solving Eigenvalue Problems Of Large-scale Symmetric Matrices

Solving eigenvalues of large-scale matrices has become the core problem in many fields,for instance,chemical engineering,computational fluid dynamics,image compression and reconstruction.At present,many specialists and scholars at home and overseas have researched eigenvalue problem of large-scale matrix,and put forward many effective algorithms,such as the Arnoldi method.This paper mainly studies the algorithms for solving eigenvalue problems of largescale real symmetric matrix.Firstly,we introduce the Krylov subspace method,the residual Arnoldi(RA)method,the shift and invert residual Arnoldi(SIRA)methodand the perfect Krylov subspace(PKS)method.And we propose an extended shift and invert residual Arnoldi algorithm according to the idea of perfect Krylov subspace method.Then the convergence of the new algorithm and its relationship with the perfect Krylov subspace algorithm are analyzed reasonably.The results of numerical experiments indicate that our raised algorithm is workable and valid,especially when the precision of the initial approximation vector is not high,and the proposed algorithm is better than the shift and invert residual Arnoldi method.