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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.12782 |
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| _version_ | 1866915859102957568 |
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| author | Gillis, Nicolas Scalone, Carmela |
| author_facet | Gillis, Nicolas Scalone, Carmela |
| contents | We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential system, whose solution is parametrized according to a nonnegative factorization. The conservation of the nonnegativity is theoretically motivated by the Perron-Frobenius theorem, while the computation of the rightmost eigenpair is motivated by two applications: (1) a new class of Markov chains, which we called Markov grids, whose transition matrices can be decomposed as the sum of Kronecker products, and (2) spatially structured systems in growth-diffusion operators arising for example in population and epidemic dynamics. Theoretical analysis and computational experiments show the effectiveness of the algorithm compared to standard approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12782 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing the Nonnegative Low-Rank Leading Eigenmatrix and its Applications to Markov Grids and Metzler Operators Gillis, Nicolas Scalone, Carmela Numerical Analysis We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential system, whose solution is parametrized according to a nonnegative factorization. The conservation of the nonnegativity is theoretically motivated by the Perron-Frobenius theorem, while the computation of the rightmost eigenpair is motivated by two applications: (1) a new class of Markov chains, which we called Markov grids, whose transition matrices can be decomposed as the sum of Kronecker products, and (2) spatially structured systems in growth-diffusion operators arising for example in population and epidemic dynamics. Theoretical analysis and computational experiments show the effectiveness of the algorithm compared to standard approaches. |
| title | Computing the Nonnegative Low-Rank Leading Eigenmatrix and its Applications to Markov Grids and Metzler Operators |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.12782 |