Variable preconditioning via quasi-Newton methods for nonlinear problems in Hilbert space

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The aim of this paper is to develop stepwise variable preconditioning for the iterative solution of monotone operator equations in Hubert space and apply it to nonlinear elliptic problems. The paper is built up to reflect the common character of preconditioned simple iterations and quasi-Newton methods. The main feature of the results is that the preconditioned are chosen via spectral equivalence. The latter can be executed in the corresponding Sobolev space in the case of elliptic problems, which helps both the construction and convergence analysis of preconditioners. This is illustrated by an example of a preconditioner using suitable domain decomposition.

Original languageEnglish
Pages (from-to)1242-1262
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number4
DOIs
Publication statusPublished - Aug 2003

Fingerprint

Sobolev spaces
Quasi-Newton Method
Hilbert spaces
Newton-Raphson method
Preconditioning
Preconditioner
Nonlinear Problem
Hilbert space
Decomposition
Nonlinear Elliptic Problems
Monotone Operator
Hubert Space
Iterative Solution
Operator Equation
Domain Decomposition
Convergence Analysis
Elliptic Problems
Sobolev Spaces
Equivalence
Iteration

Keywords

  • Iterative methods in Hilbert space
  • Nonlinear elliptic problems
  • Quasi-Newton methods
  • Variable preconditioning

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Variable preconditioning via quasi-Newton methods for nonlinear problems in Hilbert space. / Karátson, J.; Faragó, I.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 4, 08.2003, p. 1242-1262.

Research output: Contribution to journalArticle

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