A new variant of Arnoldi method for approximation of eigenpairs
作者：
Highlights：
• Arnoldi method is known to approximate eigenvalues but not the corresponding eigenvectors.
• The refined Arnoldi method approximates the eigenvectors, which requires solving a singular value problem.
• It is revealed that the Arnoldi method is incapable of balancing the components of a Ritz vector and its orthogonal complement.
• A new variant of Arnoldi method is suggested via minimizing the residual of the resultant vector of a Ritz vector and one chosen from the orthogonal complement of it.
• This heuristic leads to solving a linear system, which is computationally cheaper than solving a singular value problem as required in the refined Arnoldi method.
• It is shown that the convergence properties of the new method are comparable with those of the refined Arnoldi method.
摘要
•Arnoldi method is known to approximate eigenvalues but not the corresponding eigenvectors.•The refined Arnoldi method approximates the eigenvectors, which requires solving a singular value problem.•It is revealed that the Arnoldi method is incapable of balancing the components of a Ritz vector and its orthogonal complement.•A new variant of Arnoldi method is suggested via minimizing the residual of the resultant vector of a Ritz vector and one chosen from the orthogonal complement of it.•This heuristic leads to solving a linear system, which is computationally cheaper than solving a singular value problem as required in the refined Arnoldi method.•It is shown that the convergence properties of the new method are comparable with those of the refined Arnoldi method.
论文关键词：65F02,Eigenvalues and eigenvectors of large matrices,Arnoldi method,Refined Arnoldi method
论文评审过程：Received 17 March 2015, Revised 19 April 2018, Available online 2 June 2018, Version of Record 17 June 2018.
论文官网地址：https://doi.org/10.1016/j.cam.2018.05.047
