A universal preconditioner for linear systems

Tom Vettenburg, Ivo M. Vellekoop

Research output: Working paper/PreprintPreprint

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Abstract

We present a universal preconditioner Γ that is applicable to all invertible linear problems Ax=y for which an approximate inverse is available. After preconditioning, the condition number depends on the norm of the discrepancy of this approximation instead of that of the original, potentially unbounded, system.

We prove that our construct is the only universal approach that ensures that ∥1−Γ−1A∥
We demonstrate and evaluate our approach for wave problems, diffusion problems, and the pantograph delay differential equation.
Original languageEnglish
Place of PublicationCornell University
PublisherarXiv
Number of pages9
DOIs
Publication statusPublished - 28 Jul 2022

Keywords

  • math.NA
  • cs.NA
  • physics.comp-ph
  • 65F08
  • accretive linear systems
  • preconditioning
  • iterative methods
  • partial differential equations
  • generalized Born series
  • Richardson iteration

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