Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems
Joint Authors
El-Alem, Mahmoud M.
Abdel-Aziz, Mohammedi R.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-07-22
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms.
When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace.
In this paper, we introduce an algorithm for solving nonlinear least squares problems.
This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step.
The computational step on the small dimensional subspace lies inside the trust region.
The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it.
A convergence theory of this algorithm is presented.
It is shown that this algorithm is globally convergent.
American Psychological Association (APA)
Abdel-Aziz, Mohammedi R.& El-Alem, Mahmoud M.. 2009. Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-17.
https://search.emarefa.net/detail/BIM-472067
Modern Language Association (MLA)
Abdel-Aziz, Mohammedi R.& El-Alem, Mahmoud M.. Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-17.
https://search.emarefa.net/detail/BIM-472067
American Medical Association (AMA)
Abdel-Aziz, Mohammedi R.& El-Alem, Mahmoud M.. Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-17.
https://search.emarefa.net/detail/BIM-472067
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-472067