Shift-invert Rational Krylov method for an operator \(\phi \)-function of an unbounded linear operator

  • Yuka HashimotoEmail author
  • Takashi Nodera
Original Paper


The product of a matrix function and a vector is used to solve evolution equations numerically. Hashimoto and Nodera (ANZIAM J 58:C149–C161, 2016) proposed the Shift-invert Rational Krylov method for computing these products. However, since matrices produced by evolution equations behave like unbounded operators in infinite-dimensional spaces, an analysis with the unbounded operator is essential. In this paper, the Shift-invert Rational Krylov method is extended to be applied to unbounded operators.


Krylov subspace method Operator function Unbounded operator \(\phi \)-function 

Mathematics Subject Classification

65F60 65M22 47A60 



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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Fundamental Science and Technology, Graduate School of Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Center for Advanced Intelligence ProjectRIKENTokyoJapan
  3. 3.Department of Mathematics, Faculty of Science and TechnologyKeio UniversityYokohamaJapan

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