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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.
2018 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 338, no 1, p. 421-431Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 338, no 1, p. 421-431
Keywords [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-149634DOI: 10.1016/j.amc.2018.05.041ISI: 000441871500033OAI: oai:DiVA.org:liu-149634DiVA, id: diva2:1232636
Available from: 2018-07-12 Created: 2018-07-12 Last updated: 2018-09-13

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The full text will be freely available from 2020-07-11 00:01
Available from 2020-07-11 00:01

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CiteExportLink to record
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Citation style
  • apa
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  • Other style
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  • de-DE
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  • nn-NB
  • sv-SE
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