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Registro Completo |
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Biblioteca(s): |
Embrapa Mandioca e Fruticultura. |
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Data corrente: |
28/08/1995 |
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Data da última atualização: |
28/08/1995 |
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Autoria: |
TAPIA, R. A. |
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Afiliação: |
Lacturer, Departmet of Mathematics, Xian Jiaotong University, Xian, Shaanxi, China. |
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Título: |
Hybrid method for nonlinear least-square problems without calculating derivatives. |
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Ano de publicação: |
1990 |
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Fonte/Imprenta: |
Journal of Optimization Theory and Applications, v.65, n.3, p.554-575, 1990. |
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Idioma: |
Inglês |
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Conteúdo: |
This paper presents a no-derivative modification of the hybrid Gauss-Newton-BFGS method for nonlinear least-square problems suggested initially by Al-Baali and Fletcher and modified later by Fletcher and Xu. The modification is made in such a way that, in a Gauss-Newton step, the Broyden's rank-one updating formula is used to obtain an approximate Jacobian and, in a BFGS step, the Jacobian is estimated using difference formulas. A set of numerical comparisons among the new hubrid method, the Gauss-Newton-Broyden method, and the finite-difference BFGS method is made and shows that the new hybrid method combines the better feature of Gauss-Newton-Broyden method and the finite-difference BFGS method. this paper also extends to the least-square problem the finite-termination property of the Broyden method, proved for a nonsigular system of equations by Gay and for the full-rank rectangular system of equations by Gerber and Luk. |
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Palavras-Chave: |
BFGS method; Finite-termination property; Gauss-newton method; Hybrid method; Nonlinear least squares. |
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Categoria do assunto: |
-- |
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Marc: |
LEADER 01498naa a2200181 a 4500
001 1646883
005 1995-08-28
008 1990 bl --- 0-- u #d
100 1 $aTAPIA, R. A.
245 $aHybrid method for nonlinear least-square problems without calculating derivatives.
260 $c1990
520 $aThis paper presents a no-derivative modification of the hybrid Gauss-Newton-BFGS method for nonlinear least-square problems suggested initially by Al-Baali and Fletcher and modified later by Fletcher and Xu. The modification is made in such a way that, in a Gauss-Newton step, the Broyden's rank-one updating formula is used to obtain an approximate Jacobian and, in a BFGS step, the Jacobian is estimated using difference formulas. A set of numerical comparisons among the new hubrid method, the Gauss-Newton-Broyden method, and the finite-difference BFGS method is made and shows that the new hybrid method combines the better feature of Gauss-Newton-Broyden method and the finite-difference BFGS method. this paper also extends to the least-square problem the finite-termination property of the Broyden method, proved for a nonsigular system of equations by Gay and for the full-rank rectangular system of equations by Gerber and Luk.
653 $aBFGS method
653 $aFinite-termination property
653 $aGauss-newton method
653 $aHybrid method
653 $aNonlinear least squares
773 $tJournal of Optimization Theory and Applications$gv.65, n.3, p.554-575, 1990.
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Embrapa Mandioca e Fruticultura (CNPMF) |
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