Result: A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems
Title:
A structured secant method based on a new quasi-Newton equation for nonlinear least squares problems
Authors:
Source:
BIT (Nordisk Tidskrift for Informationsbehandling). 43(1):217-229
Publisher Information:
Dordrecht: Springer, 2003.
Publication Year:
2003
Physical Description:
print, 8 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Programmation mathématique, Mathematical programming, Approximation non linéaire, Non linear approximation, Aproximación no lineal, Méthode moindre carré, Least squares method, Método cuadrado menor, Méthode numérique, Numerical method, Método numérico, Méthode quasi Newton, Quasi Newton method, Método cuasi Newton, Programmation mathématique, Mathematical programming, Programación matemática, Taux convergence, Convergence rate, Relación convergencia, Convergence quadratique, Quadratic convergence, Convergencia Mosco, Convergence super linéaire, Super linear convergence, Méthode sécante, Secant method, Ordre approximation, Approximation order
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, City University of Hong Kong, Hong-Kong
Department of Applied Mathematics, Beijing Polytechnic University, Beijing 100022, China
Department of Applied Mathematics, Beijing Polytechnic University, Beijing 100022, China
ISSN:
0006-3835
Rights:
Copyright 2003 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Operational research. Management
Operational research. Management
Accession Number:
edscal.14837052
Database:
PASCAL Archive
Further Information
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.