Eigenvalue Decomposition Based Modified Newton Algorithm

DOI

10.2991/iccsee.2013.511How to use a DOI?

Keywords

Newton algorithm, eigenvalue decomposition, convergence, convergence domain

Abstract

When the Hessian matrix is not positive, the Newton direction maybe not the descending direction. A new method named eigenvalue decomposition based modified Newton algorithm is presented, which first takes eigenvalue decomposition on the Hessian matrix, then replaces the negative eigenvalues with their absolutely values, finally reconstruct Hessian matrix and modify searching direction. The new searching direction is always the descending direction, and the convergence of the algorithm is proved and conclusion on convergence rate is presented qualitatively. At last, a numerical experiment is given for comparing the convergence domains of modified algorithm and classical algorithm.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Wenjun Wang
AU  - Jubo Zhu
AU  - Xiaojun Duan
PY  - 2013/03
DA  - 2013/03
TI  - Eigenvalue Decomposition Based Modified Newton Algorithm
BT  - Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)
PB  - Atlantis Press
SP  - 2032
EP  - 2035
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccsee.2013.511
DO  - 10.2991/iccsee.2013.511
ID  - Wang2013/03
ER  -