An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices
The irreducibility of nonnegative matrices is an important condition for the diagonal transformation algorithm to succeed. In this paper, we introduce zero symmetry to replace the irreducibility of nonnegative matrices and propose an improved diagonal transformation algorithm for finding the maximum...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/8/1707 |
| _version_ | 1797431724092686336 |
|---|---|
| author | Gang Wang Jinfa Liu |
| author_facet | Gang Wang Jinfa Liu |
| author_sort | Gang Wang |
| collection | DOAJ |
| description | The irreducibility of nonnegative matrices is an important condition for the diagonal transformation algorithm to succeed. In this paper, we introduce zero symmetry to replace the irreducibility of nonnegative matrices and propose an improved diagonal transformation algorithm for finding the maximum eigenvalue without any partitioning. The improved algorithm retains all of the benefits of the diagonal transformation algorithm while having fewer computations. Numerical examples are reported to show the efficiency of the proposed algorithm. As an application, the improved algorithm is used to check whether a zero symmetric matrix is an <i>H</i>-matrix. |
| first_indexed | 2024-03-09T09:49:26Z |
| format | Article |
| id | doaj.art-e3eb639403d048cbb2e3f978ea0c1268 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T09:49:26Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e3eb639403d048cbb2e3f978ea0c12682023-12-02T00:22:09ZengMDPI AGSymmetry2073-89942022-08-01148170710.3390/sym14081707An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative MatricesGang Wang0Jinfa Liu1School of Management Science, Qufu Normal University, Rizhao 276800, ChinaSchool of Management Science, Qufu Normal University, Rizhao 276800, ChinaThe irreducibility of nonnegative matrices is an important condition for the diagonal transformation algorithm to succeed. In this paper, we introduce zero symmetry to replace the irreducibility of nonnegative matrices and propose an improved diagonal transformation algorithm for finding the maximum eigenvalue without any partitioning. The improved algorithm retains all of the benefits of the diagonal transformation algorithm while having fewer computations. Numerical examples are reported to show the efficiency of the proposed algorithm. As an application, the improved algorithm is used to check whether a zero symmetric matrix is an <i>H</i>-matrix.https://www.mdpi.com/2073-8994/14/8/1707improved diagonal transformation algorithmzero symmetric reducible nonnegative matricesmaximum eigenvalueH-matrix |
| spellingShingle | Gang Wang Jinfa Liu An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices Symmetry improved diagonal transformation algorithm zero symmetric reducible nonnegative matrices maximum eigenvalue H-matrix |
| title | An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices |
| title_full | An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices |
| title_fullStr | An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices |
| title_full_unstemmed | An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices |
| title_short | An Improved Diagonal Transformation Algorithm for the Maximum Eigenvalue of Zero Symmetric Nonnegative Matrices |
| title_sort | improved diagonal transformation algorithm for the maximum eigenvalue of zero symmetric nonnegative matrices |
| topic | improved diagonal transformation algorithm zero symmetric reducible nonnegative matrices maximum eigenvalue H-matrix |
| url | https://www.mdpi.com/2073-8994/14/8/1707 |
| work_keys_str_mv | AT gangwang animproveddiagonaltransformationalgorithmforthemaximumeigenvalueofzerosymmetricnonnegativematrices AT jinfaliu animproveddiagonaltransformationalgorithmforthemaximumeigenvalueofzerosymmetricnonnegativematrices AT gangwang improveddiagonaltransformationalgorithmforthemaximumeigenvalueofzerosymmetricnonnegativematrices AT jinfaliu improveddiagonaltransformationalgorithmforthemaximumeigenvalueofzerosymmetricnonnegativematrices |