Eigenvalue Decomposition-Based Modified Newton Algorithm
Joint Authors
Wang, Wen-jun
Zhu, Ju-bo
Duan, Xiao-jun
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-26
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
When the Hessian matrix is not positive, the Newton direction may not be the descending direction.
A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction.
The new searching direction is always the descending direction.
The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively.
Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.
American Psychological Association (APA)
Wang, Wen-jun& Zhu, Ju-bo& Duan, Xiao-jun. 2013. Eigenvalue Decomposition-Based Modified Newton Algorithm. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-1009698
Modern Language Association (MLA)
Wang, Wen-jun…[et al.]. Eigenvalue Decomposition-Based Modified Newton Algorithm. Mathematical Problems in Engineering No. 2013 (2013), pp.1-4.
https://search.emarefa.net/detail/BIM-1009698
American Medical Association (AMA)
Wang, Wen-jun& Zhu, Ju-bo& Duan, Xiao-jun. Eigenvalue Decomposition-Based Modified Newton Algorithm. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-1009698
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1009698