A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems

J. Z. Zhang; Y. Xue; K. Zhang

doi:10.1023/A:1023665409152

A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems

J. Z. Zhang
, Y. Xue
, K. Zhang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

In this paper, a new quasi-Newton equation is applied to the structured secant methods for nonlinear least squares problems. We show that the new equation is better than the original quasi-Newton equation as it provides a more accurate approximation to the second order information. Furthermore, combining the new quasi-Newton equation with a "product structure", a new algorithm is established. It is shown that the resulting algorithm is quadratically convergent for the zero-residual case and superlinearly convergent for the nonzero-residual case. In order to compare the new algorithm with some related methods, our preliminary numerical experiments are also reported.
© 2003 Kluwer Academic Publishers

Original language	English
Pages (from-to)	217-229
Journal	BIT Numerical Mathematics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1023/A:1023665409152
Publication status	Published - Mar 2003
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

Supported by the City University of Hong Kong under its Strategic Research Grant 7000944.

Research Keywords

Nonlinear least squares
Quadratic convergence
Quasi-Newton equation
Structured secant method
Superlinear convergence

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10.1023/A:1023665409152

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title = "A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems",

abstract = "In this paper, a new quasi-Newton equation is applied to the structured secant methods for nonlinear least squares problems. We show that the new equation is better than the original quasi-Newton equation as it provides a more accurate approximation to the second order information. Furthermore, combining the new quasi-Newton equation with a {"}product structure{"}, a new algorithm is established. It is shown that the resulting algorithm is quadratically convergent for the zero-residual case and superlinearly convergent for the nonzero-residual case. In order to compare the new algorithm with some related methods, our preliminary numerical experiments are also reported. {\textcopyright} 2003 Kluwer Academic Publishers",

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AU - Xue, Y.

AU - Zhang, K.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - In this paper, a new quasi-Newton equation is applied to the structured secant methods for nonlinear least squares problems. We show that the new equation is better than the original quasi-Newton equation as it provides a more accurate approximation to the second order information. Furthermore, combining the new quasi-Newton equation with a "product structure", a new algorithm is established. It is shown that the resulting algorithm is quadratically convergent for the zero-residual case and superlinearly convergent for the nonzero-residual case. In order to compare the new algorithm with some related methods, our preliminary numerical experiments are also reported. © 2003 Kluwer Academic Publishers

AB - In this paper, a new quasi-Newton equation is applied to the structured secant methods for nonlinear least squares problems. We show that the new equation is better than the original quasi-Newton equation as it provides a more accurate approximation to the second order information. Furthermore, combining the new quasi-Newton equation with a "product structure", a new algorithm is established. It is shown that the resulting algorithm is quadratically convergent for the zero-residual case and superlinearly convergent for the nonzero-residual case. In order to compare the new algorithm with some related methods, our preliminary numerical experiments are also reported. © 2003 Kluwer Academic Publishers

KW - Nonlinear least squares

KW - Quadratic convergence

KW - Quasi-Newton equation

KW - Structured secant method

KW - Superlinear convergence

UR - https://www.scopus.com/pages/publications/4043053592

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U2 - 10.1023/A:1023665409152

DO - 10.1023/A:1023665409152

M3 - RGC 21 - Publication in refereed journal

SN - 0006-3835

VL - 43

SP - 217

EP - 229

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 1

ER -

A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems

Abstract

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Research Keywords

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