An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices

In this paper, we propose an improved power algorithm for finding maximal eigenvalues. Without any partition, we can get the maximal eigenvalue and show that the modified power algorithm is convergent for zero symmetric reducible nonnegative matrices. Numerical results are reported to demonstrate th...

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Main Authors:	Gang Wang, Lihong Sun
Format:	Article
Language:	English
Published:	Hindawi Limited 2018-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2018/6438106

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spelling	doaj-1860caff0d344b548c6b0dcf7d539e532020-11-24T22:58:12ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/64381066438106An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative MatricesGang Wang0Lihong Sun1School of Management Science, Qufu Normal University, Rizhao, Shandong, 276800, ChinaSchool of Management Science, Qufu Normal University, Rizhao, Shandong, 276800, ChinaIn this paper, we propose an improved power algorithm for finding maximal eigenvalues. Without any partition, we can get the maximal eigenvalue and show that the modified power algorithm is convergent for zero symmetric reducible nonnegative matrices. Numerical results are reported to demonstrate the effectiveness of the modified power algorithm. Finally, a modified algorithm is proposed to test the positive definiteness (positive semidefiniteness) of Z-matrices.http://dx.doi.org/10.1155/2018/6438106
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Gang Wang Lihong Sun
spellingShingle	Gang Wang Lihong Sun An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices Mathematical Problems in Engineering
author_facet	Gang Wang Lihong Sun
author_sort	Gang Wang
title	An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices
title_short	An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices
title_full	An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices
title_fullStr	An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices
title_full_unstemmed	An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices
title_sort	efficient algorithm for finding the maximal eigenvalue of zero symmetric nonnegative matrices
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2018-01-01
description	In this paper, we propose an improved power algorithm for finding maximal eigenvalues. Without any partition, we can get the maximal eigenvalue and show that the modified power algorithm is convergent for zero symmetric reducible nonnegative matrices. Numerical results are reported to demonstrate the effectiveness of the modified power algorithm. Finally, a modified algorithm is proposed to test the positive definiteness (positive semidefiniteness) of Z-matrices.
url	http://dx.doi.org/10.1155/2018/6438106
work_keys_str_mv	AT gangwang anefficientalgorithmforfindingthemaximaleigenvalueofzerosymmetricnonnegativematrices AT lihongsun anefficientalgorithmforfindingthemaximaleigenvalueofzerosymmetricnonnegativematrices AT gangwang efficientalgorithmforfindingthemaximaleigenvalueofzerosymmetricnonnegativematrices AT lihongsun efficientalgorithmforfindingthemaximaleigenvalueofzerosymmetricnonnegativematrices
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An Efficient Algorithm for Finding the Maximal Eigenvalue of Zero Symmetric Nonnegative Matrices

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