Parallel multi-splitting methods for nonlinear quadratic matrix equation

Author

Lin, Xiao-Lin ; Shi, Sheng-Nan

Author_Institution

Fac. of Sci., Shaanxi Univ. Of Sci. & Technol., Xi´´an, China

Volume

1

fYear

2010

fDate

28-31 Aug. 2010

Firstpage

11

Lastpage

14

Abstract

In this paper, motivated by multi-splitting methods, a nonlinear method for solving the quadratic matrix equation (QME) is constructed. Meanwhile, nonlinear multi-splitting algorithm and nonlinear multi-splitting Newton algorithm are presented to find the solution to QME. Then under suitable conditions, the local linear and quadratic convergence of the algorithms are proved respectively. In the end, a numerical result is given to show the feasibility and effectiveness of these algorithms.

Keywords

Newton method; convergence of numerical methods; eigenvalues and eigenfunctions; matrix algebra; nonlinear equations; QME; linear convergence; nonlinear multisplitting Newton algorithm; nonlinear quadratic matrix equation; parallel multisplitting method; quadratic convergence; Algorithm design and analysis; Convergence; Eigenvalues and eigenfunctions; Equations; Markov processes; Mathematical model; Newton method; Integral mean-value theorem; Newton method; Parallel multi-splitting; Quadratic matrix equation;

fLanguage

English

Publisher

ieee

Conference_Titel

Geoscience and Remote Sensing (IITA-GRS), 2010 Second IITA International Conference on

Conference_Location

Qingdao

Print_ISBN

978-1-4244-8514-7

Type

conf

DOI

10.1109/IITA-GRS.2010.5603151

Filename

5603151