Improved Newton's method with exact line searches to solve quadratic matrix equation

Authors:
Jian-hui Long;Xi-yan Hu;Lei Zhang
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
Cited 1

Solution of the Sylvester matrix equation AXBT + CXDT = E

ACM Transactions on Mathematical Software (TOMS)
Algorithm 598: an algorithm to compute solvent of the matrix equation AX2 + BX + C = 0

ACM Transactions on Mathematical Software (TOMS)
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches

SIAM Journal on Matrix Analysis and Applications
The Quadratic Eigenvalue Problem

SIAM Review

Linear-quadratic optimal control strategy for periodic-review inventory systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper, we study the matrix equation AX^2+BX+C=0, where A,B and C are square matrices. We give two improved algorithms which are better than Newton's method with exact line searches to calculate the solution. Some numerical examples are reported to illustrate our algorithms.