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Fast Parallel Matrix Inversion Algorithms
Abstract
The parallel arithmetic complexities of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix are shown to have the same growth rate. Algorithms are given that compute these problems in $O(\log ^2 n)$ steps using a number of processors polynomial in n. (n is the order of the matrix of the problem.)
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Cited by
Map-Reduce for Machine Learning on Multicore
Chu, C.-T., Kim, S. K., Lin, Y.-A., Yu, Y., Bradski, G., Ng, A. Y., & Olukotun, K. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0040 · Cited by 1,229
Quantum machine learning: a classical perspective
Ciliberto, C., Herbster, M., Ialongo, A. D., Pontil, M., Rocchetto, A., Severini, S., & Wossnig, L. (2018) · Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rspa.2017.0551 · Cited by 518
Completeness Classes in Algebra
Valiant, L. G. (1979) · ACM eBooks · doi:10.1145/3749740.3749750 · Cited by 465
Quantum advantage with shallow circuits
Bravyi, S., Gosset, D., & König, R. (2018) · Science · doi:10.1126/science.aar3106 · Cited by 406
Matching is as easy as matrix inversion
Mulmuley, K., Vazirani, U. V., & Vazirani, V. V. (1987) · Combinatorica · doi:10.1007/bf02579206 · Cited by 388
Metadata
- Authors
- Csanky, L.
- Venue
- SIAM Journal on Computing
- Published
- 1976-12
- Volume
- 5
- Issue
- 4
- Pages
- 618-623
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2113097540
- Cited by
- 397
- References
- 0
- FWCI
- 6.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- Csanky, L. (1976). Fast Parallel Matrix Inversion Algorithms. SIAM Journal on Computing. https://doi.org/10.1137/0205040
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