R3GMRES: including prior information in GMRES-type methods for discrete inverse problems

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Abstract

Lothar Reichel and his collaborators proposed several iterative algorithms that augment the underlying Krylov subspace with an additional low-dimensional subspace in order to produce improved regularized solutions. We take a closer look at this approach and investigate a particular Regularized Range-Restricted GMRES method, R3GMRES, with a subspace that represents prior information about the solution. We discuss the implementation of this approach and demonstrate its advantage by means of several test problems.
Original languageEnglish
JournalElectronic Transactions on Numerical Analysis
Volume42
Pages (from-to)136-146
ISSN1068-9613
Publication statusPublished - 2014

Keywords

  • Inverse problems
  • Regularizing iterations
  • Large-scale problems
  • Prior information

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