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Methods of the secant type for systems of equations with symmetric Jacobian matrix
Computing Center, USSR Academy of Sciences, Moscow.ORCID iD: 0000-0003-1836-4200
1983 (English)In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 6, no 2, 183-195 p.Article in journal (Refereed) Published
Abstract [en]

Symmetric methods (SS methods) of the secant type are proposed for systems of equations with symmetric Jacobian matrix. The SSI and SS2 methods generate sequences of symmetric matrices J and H which approximate the Jacobian matrix and inverse one, respectively. Rank-two quasi-Newton formulas for updating J and H are derived. The structure of the approximations J and H is better than the structure of the corresponding approximations in the traditional secant method because the SS methods take into account symmetry of the Jacobian matrix. Furthermore, the new methods retain the main properties of the traditional secant method, namely, J and H-1are consistent approximations to the Jacobian matrix; the SS methods converge superlinearly; the sequential (n + 1)-point SS methods have the R-order at least equal to the positive root of tn+1-tn-1=0.

Place, publisher, year, edition, pages
Taylor & Francis, 1983. Vol. 6, no 2, 183-195 p.
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-78875DOI: 10.1080/01630568308816160OAI: diva2:536332
Available from: 2012-06-21 Created: 2012-06-21 Last updated: 2015-06-02

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Burdakov, Oleg
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