TY - JOUR
A2 - Zhou, Jian Guo
AU - Wang, Wen-jun
AU - Zhu, Ju-bo
AU - Duan, Xiao-jun
PY - 2013
DA - 2013/03/26
TI - Eigenvalue Decomposition-Based Modified Newton Algorithm
SP - 523895
VL - 2013
AB - 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.
SN - 1024-123X
UR - https://doi.org/10.1155/2013/523895
DO - 10.1155/2013/523895
JF - Mathematical Problems in Engineering
PB - Hindawi Publishing Corporation
KW -
ER -