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Extended and rational Hessenberg methods for the evaluation of matrix functions

  • Z. Ramezani
  • F. Toutounian
Article
  • 78 Downloads

Abstract

Some Krylov subspace methods for approximating the action of matrix functions are presented in this paper. The main idea of these techniques is to project the approximation problem onto a subspace of much smaller dimension. Then the matrix function operation is performed with a much smaller matrix. These methods are projection methods that use the Hessenberg process to generate bases of the approximation spaces. We also use the introduced methods to solve shifted linear systems. Some numerical experiments are presented in order to show the efficiency of the proposed methods.

Keywords

Krylov subspace methods Extended Krylov subspace Rational Krylov subspace Hessenberg process Matrix function Shifted linear system 

Mathematics Subject Classification

65F10 

Notes

Acknowledgements

We would like to thank the referees for their valuable remarks and helpful suggestions.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, School of Mathematical SciencesFerdowsi University of MashhadMashhadIran
  2. 2.The Center of Excellence on Modeling and Control SystemsFerdowsi University of MashhadMashhadIran

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