Numerical Algorithms

, Volume 82, Issue 3, pp 791–807 | Cite as

Filtered Krylov-like sequence method for symmetric eigenvalue problems

  • Cun-Qiang MiaoEmail author
Original Paper


In this paper, by introducing a class of filtered Krylov-like subspaces, we present the filtered Krylov-like sequence method for computing one extreme eigenvalue and the corresponding eigenvector of symmetric matrices. The filtered Krylov-like sequence method can be desired to behave, practically, more effective and robust than the standard Krylov subspace method. We specifically select two kinds of polynomial filters, and relate them to some well-known methods. Some numerical experiments are carried out to demonstrate the convergence properties and the competitiveness of the new method.


Eigenvalue Eigenvector Filtered Krylov-like subspace Polynomial filter Symmetric matrix 

Mathematics Subject Classification (2010)

65F15 65N25 


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The author is very much indebted to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper.

Funding information

This study is supported by the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2017RCJJ067) and the Natural Science Foundation of Shandong Province (No. ZR2018BG002), P.R. China.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoPeople’s Republic of China

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