Improved Newton's method with exact line searches to solve quadratic matrix equation
type: Item
instance of: scholarly article
title: Improved Newton's method with exact line searches to solve quadratic matrix equation
zbMATH Open document ID: 1159.65044
author: Lei Zhang
author: Jian-hui Long
author: Xiyan Hu
published in: Journal of Computational and Applied Mathematics
publication date: 2008-11-18T00:00:00Z
review text: A method for solving the matrix equation \(AX^2 + BX + C=0\) is given. There are two main contributions: First, the incorporation of Newton's method with exact new line searches is to reduce the computational cost, and second, the use of the technique of \textit{V. E. Shamanskij} [Ukrain Math. Z. 19, No.~1, 133--138 (1967; Zbl 0176.13802)] to get a faster rate of convergence. Theoretical and computational results are presented to show the efficiency of the proposed method.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5368395
zbMATH Keywords: quadratic matrix equation
zbMATH Keywords: Newton's method
zbMATH Keywords: exact line search
zbMATH Keywords: numerical examples
reviewed by: R. P. Tewarson
describes a project that uses: SQUINT
MaRDI profile type: Publication
full work available at URL: j.cam.2007.12.018
OpenAlex ID: W1981945670
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DOI: 10.1016/J.CAM.2007.12.018
description: scientific article; zbMATH DE number 5368395