Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices
In this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds. We also refer to their equality cases if the matrix is irreducibl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-04-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2022-0165 |
| _version_ | 1811222928364142592 |
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| author | Adam Maria Aretaki Aikaterini |
| author_facet | Adam Maria Aretaki Aikaterini |
| author_sort | Adam Maria |
| collection | DOAJ |
| description | In this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds. We also refer to their equality cases if the matrix is irreducible, and we present numerical examples to make comparisons among them. Finally, we provide an application to special matrices such as the generalized Fibonacci matrices, which are widely used in applied mathematics and computer science problems. |
| first_indexed | 2024-04-12T08:23:09Z |
| format | Article |
| id | doaj.art-842e4c9fbc314a298f4220f5676eea99 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-04-12T08:23:09Z |
| publishDate | 2022-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-842e4c9fbc314a298f4220f5676eea992022-12-22T03:40:28ZengDe GruyterSpecial Matrices2300-74512022-04-0110130832610.1515/spma-2022-0165Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matricesAdam Maria0Aretaki Aikaterini1Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou str., P.O. 35131 Lamia, GreeceDepartment of Mathematics, University of Thessaly, 3rd km P.E.O. Lamia-Athina, P.O. 35100 Lamia, GreeceIn this article, we determine upper and lower bounds for the spectral radius of nonnegative matrices. Introducing the notion of average 4-row sum of a nonnegative matrix, we extend various existing formulas for spectral radius bounds. We also refer to their equality cases if the matrix is irreducible, and we present numerical examples to make comparisons among them. Finally, we provide an application to special matrices such as the generalized Fibonacci matrices, which are widely used in applied mathematics and computer science problems.https://doi.org/10.1515/spma-2022-0165nonnegative matrixspectral radius4-row sumaverage 4-row sumgeneralized fibonacci matrix15a1815a4211b39 |
| spellingShingle | Adam Maria Aretaki Aikaterini Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices Special Matrices nonnegative matrix spectral radius 4-row sum average 4-row sum generalized fibonacci matrix 15a18 15a42 11b39 |
| title | Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices |
| title_full | Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices |
| title_fullStr | Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices |
| title_full_unstemmed | Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices |
| title_short | Bounds for the spectral radius of nonnegative matrices and generalized Fibonacci matrices |
| title_sort | bounds for the spectral radius of nonnegative matrices and generalized fibonacci matrices |
| topic | nonnegative matrix spectral radius 4-row sum average 4-row sum generalized fibonacci matrix 15a18 15a42 11b39 |
| url | https://doi.org/10.1515/spma-2022-0165 |
| work_keys_str_mv | AT adammaria boundsforthespectralradiusofnonnegativematricesandgeneralizedfibonaccimatrices AT aretakiaikaterini boundsforthespectralradiusofnonnegativematricesandgeneralizedfibonaccimatrices |