Approximate square-free part and decomposition
Square-free decomposition is one of fundamental computations for polynomials. However, any conventional algorithm may not work for polynomials with a priori errors on their coefficients. There are mainly two approaches to overcome this empirical situation: approximate polynomial GCD (greatest common...
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| Published in | Journal of symbolic computation Vol. 104; pp. 402 - 418 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0747-7171 1095-855X 1095-855X |
| DOI | 10.1016/j.jsc.2020.08.004 |
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| Abstract | Square-free decomposition is one of fundamental computations for polynomials. However, any conventional algorithm may not work for polynomials with a priori errors on their coefficients. There are mainly two approaches to overcome this empirical situation: approximate polynomial GCD (greatest common divisor) and the nearest singular polynomial. In this paper, we show that these known approaches are not enough for detecting the nearest square-free part (which has no multiple roots) within the given upper bound of perturbations (a priori errors), and we propose a new definition and a new method to detect a square-free part and its decomposition numerically by following a recent framework of approximate polynomial GCD. |
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| AbstractList | Square-free decomposition is one of fundamental computations for polynomials. However, any conventional algorithm may not work for polynomials with a priori errors on their coefficients. There are mainly two approaches to overcome this empirical situation: approximate polynomial GCD (greatest common divisor) and the nearest singular polynomial. In this paper, we show that these known approaches are not enough for detecting the nearest square-free part (which has no multiple roots) within the given upper bound of perturbations (a priori errors), and we propose a new definition and a new method to detect a square-free part and its decomposition numerically by following a recent framework of approximate polynomial GCD. |
| Author | Nagasaka, Kosaku |
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| Cites_doi | 10.1016/S0024-3795(02)00505-0 10.1137/0711083 10.1016/j.laa.2005.06.028 10.1007/s10208-015-9256-x 10.1145/3096730.3096733 10.1007/BF03167469 10.1007/s10898-006-9119-8 10.1016/j.tcs.2012.10.027 10.1006/jsco.1998.0233 10.1016/j.tcs.2008.09.003 |
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| Title | Approximate square-free part and decomposition |
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