Bi-parametric operator preconditioning

Paul Escapil-Inchauspé, Carlos Jerez-Hanckes

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We extend the operator preconditioning framework Hiptmair (2006) [10] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing numerical approximations. By considering different perturbation parameters for the original form and its preconditioner, our bi-parametric abstract setting leads to robust and controlled schemes. For Hilbert spaces, we derive exhaustive linear and super-linear convergence estimates for iterative solvers, such as h-independent convergence bounds, when preconditioning with low-accuracy or, equivalently, with highly compressed approximations.

Original languageEnglish
Pages (from-to)220-232
Number of pages13
JournalComputers and Mathematics with Applications
StatePublished - 15 Nov 2021
Externally publishedYes


  • Galerkin methods
  • Iterative linear solvers
  • Numerical approximation
  • Operator preconditioning


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