liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Multipoint secant and interpolation methods with nonmonotone line search for solving systems of nonlinear equations
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .ORCID iD: 0000-0003-1836-4200
University of Science and Technology of Mazandaran, Behshar, Iran.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the information about the Jacobian matrix gathered at the previous iterations, these methods are especially efficient in the case of expensive functions. They are known to be local and superlinearly convergent. We combine these methods with the nonmonotone line search proposed by Li and Fukushima (2000), and study global and superlinear convergence of this combination. Results of numerical experiments are presented. They indicate that the multipoint secant and interpolation methods tend to be more robust and efficient than Broyden's method globalized in the same way.

Keyword [en]
Systems of nonlinear equations, Quasi-Newton methods, Multipoint secant methods, Interpolation methods, Global convergence, Superlinear convergence
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143404OAI: oai:DiVA.org:liu-143404DiVA: diva2:1162654
Available from: 2017-12-05 Created: 2017-12-05 Last updated: 2017-12-05

Open Access in DiVA

No full text in DiVA

Other links

https://arxiv.org/abs/1712.01142

Search in DiVA

By author/editor
Burdakov, Oleg
By organisation
The Institute of TechnologyOptimization
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf