A Monte Carlo algorithm for efficient large matrix inversion
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2004
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| _version_ | 1866914099077578752 |
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| author | Garcia-Cortes, L. A. Cabrillo, C. |
| author_facet | Garcia-Cortes, L. A. Cabrillo, C. |
| contents | This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously reported algorithm for hermitian matrices inversion based in only one draw. The use of two draws allows the inversion on non-hermitian matrices. Both the conditions for convergence and the rate of convergence are similar to the Gauss-Seidel algorithm. Results on two examples are presented, a real non-symmetric matrix related to quantitative genetics and a complex non-hermitian matrix relevant for physicists. Compared with other Monte Carlo algorithms it reveals a large reduction of the processing time showing eight times faster processing in the examples studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cs_0412107 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | A Monte Carlo algorithm for efficient large matrix inversion Garcia-Cortes, L. A. Cabrillo, C. Data Structures and Algorithms Numerical Analysis High Energy Physics - Lattice This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously reported algorithm for hermitian matrices inversion based in only one draw. The use of two draws allows the inversion on non-hermitian matrices. Both the conditions for convergence and the rate of convergence are similar to the Gauss-Seidel algorithm. Results on two examples are presented, a real non-symmetric matrix related to quantitative genetics and a complex non-hermitian matrix relevant for physicists. Compared with other Monte Carlo algorithms it reveals a large reduction of the processing time showing eight times faster processing in the examples studied. |
| title | A Monte Carlo algorithm for efficient large matrix inversion |
| topic | Data Structures and Algorithms Numerical Analysis High Energy Physics - Lattice |
| url | https://arxiv.org/abs/cs/0412107 |