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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02553 |
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| _version_ | 1866909524597669888 |
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| author | Wang, Ying Ephremidze, Lasha Reyes, Ronaldo Garcıa Valdes-Sosa, Pedro |
| author_facet | Wang, Ying Ephremidze, Lasha Reyes, Ronaldo Garcıa Valdes-Sosa, Pedro |
| contents | Spectral factorization is a powerful mathematical tool with diverse applications in signal processing and beyond. The Janashia-Lagvilava method has emerged as a leading approach for matrix spectral factorization. In this paper, we extend a central equation of the method to the non-commutative case, enabling polynomial coefficients to be represented in block matrix form while preserving the equation's fundamental structure. This generalization results in an exponential speedup for high-dimensional matrices. Our approach addresses challenges in factorizing massive-dimensional matrices encountered in neural data analysis and other practical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Speedup of the Janashia-Lagvilava Matrix Spectral Factorization Algorithm Wang, Ying Ephremidze, Lasha Reyes, Ronaldo Garcıa Valdes-Sosa, Pedro Complex Variables 47A68 Spectral factorization is a powerful mathematical tool with diverse applications in signal processing and beyond. The Janashia-Lagvilava method has emerged as a leading approach for matrix spectral factorization. In this paper, we extend a central equation of the method to the non-commutative case, enabling polynomial coefficients to be represented in block matrix form while preserving the equation's fundamental structure. This generalization results in an exponential speedup for high-dimensional matrices. Our approach addresses challenges in factorizing massive-dimensional matrices encountered in neural data analysis and other practical applications. |
| title | Exponential Speedup of the Janashia-Lagvilava Matrix Spectral Factorization Algorithm |
| topic | Complex Variables 47A68 |
| url | https://arxiv.org/abs/2503.02553 |