Globally and superlinearly convergent inexact Newton-Krylov algorithms for solving nonsmooth equations

Jinhai Chen, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

This paper presents some variants of the inexact Newton method for solving systems of nonlinear equations defined by locally Lipschitzian functions. These methods use variants of Newton's iteration in association with Krylov subspace methods for solving the Jacobian linear systems. Global convergence of the proposed algorithms is established under a nonmonotonic backtracking strategy. The local convergence based on the assumptions of semismoothness and BD-regularity at the solution is characterized, and the way to choose an inexact forcing sequence that preserves the rapid convergence of the proposed methods is also indicated. Numerical examples are given to show the practical viability of these approaches.
Original languageEnglish
Pages (from-to)155-174
Number of pages20
JournalNumerical Linear Algebra with Applications
Volume17
Issue number1
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • Global convergence
  • Inexact newton method
  • Krylov subspace methods
  • Nonmonotonic technique
  • Nonsmooth analysis
  • Superlinear convergence

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

Cite this