An algorithm for calculating spectral radius of s-index weakly positive tensors
In this paper, we introduced $ s $-index weakly positive tensors and discussed the calculation of the spectral radius of this kind of nonnegative tensors. Using the diagonal similarity transformation of tensor and Perron-Frobenius theory of nonnegative tensor, the calculation method of the maximum $...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024012?viewType=HTML |
| _version_ | 1827587992426905600 |
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| author | Panpan Liu Hongbin Lv |
| author_facet | Panpan Liu Hongbin Lv |
| author_sort | Panpan Liu |
| collection | DOAJ |
| description | In this paper, we introduced $ s $-index weakly positive tensors and discussed the calculation of the spectral radius of this kind of nonnegative tensors. Using the diagonal similarity transformation of tensor and Perron-Frobenius theory of nonnegative tensor, the calculation method of the maximum $ H $-eigenvalue of $ s $-index weakly positive tensors was given. A variable parameter was introduced in each iteration of the algorithm, which is equivalent to a translation transformation of the tensor in each iteration to improve the calculation speed. At the same time, it was proved that the algorithm is linearly convergent for the calculation of the spectral radius of $ s $-index weakly positive tensors. The final numerical example shows the effectiveness of the algorithm. |
| first_indexed | 2024-03-09T00:25:57Z |
| format | Article |
| id | doaj.art-0f06a33435ba45eebc90146c99741ddf |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-09T00:25:57Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-0f06a33435ba45eebc90146c99741ddf2023-12-12T01:31:47ZengAIMS PressAIMS Mathematics2473-69882024-01-019120521710.3934/math.2024012An algorithm for calculating spectral radius of s-index weakly positive tensorsPanpan Liu0Hongbin Lv1School of Mathematics and Statistics, Beihua University, Jilin 132013, ChinaSchool of Mathematics and Statistics, Beihua University, Jilin 132013, ChinaIn this paper, we introduced $ s $-index weakly positive tensors and discussed the calculation of the spectral radius of this kind of nonnegative tensors. Using the diagonal similarity transformation of tensor and Perron-Frobenius theory of nonnegative tensor, the calculation method of the maximum $ H $-eigenvalue of $ s $-index weakly positive tensors was given. A variable parameter was introduced in each iteration of the algorithm, which is equivalent to a translation transformation of the tensor in each iteration to improve the calculation speed. At the same time, it was proved that the algorithm is linearly convergent for the calculation of the spectral radius of $ s $-index weakly positive tensors. The final numerical example shows the effectiveness of the algorithm.https://www.aimspress.com/article/doi/10.3934/math.2024012?viewType=HTMLirreducible nonnegative tensor$ s $-index weakly positive tensor$ h $-eigenvaluenumerical algorithm |
| spellingShingle | Panpan Liu Hongbin Lv An algorithm for calculating spectral radius of s-index weakly positive tensors AIMS Mathematics irreducible nonnegative tensor $ s $-index weakly positive tensor $ h $-eigenvalue numerical algorithm |
| title | An algorithm for calculating spectral radius of s-index weakly positive tensors |
| title_full | An algorithm for calculating spectral radius of s-index weakly positive tensors |
| title_fullStr | An algorithm for calculating spectral radius of s-index weakly positive tensors |
| title_full_unstemmed | An algorithm for calculating spectral radius of s-index weakly positive tensors |
| title_short | An algorithm for calculating spectral radius of s-index weakly positive tensors |
| title_sort | algorithm for calculating spectral radius of s index weakly positive tensors |
| topic | irreducible nonnegative tensor $ s $-index weakly positive tensor $ h $-eigenvalue numerical algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024012?viewType=HTML |
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