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Approximate square-free part and decomposition.
- Source :
-
Journal of Symbolic Computation . May2021, Vol. 104, p402-418. 17p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*DEFINITIONS
*POLYNOMIALS
*MATHEMATICAL decomposition
Subjects
Details
- Language :
- English
- ISSN :
- 07477171
- Volume :
- 104
- Database :
- Academic Search Index
- Journal :
- Journal of Symbolic Computation
- Publication Type :
- Academic Journal
- Accession number :
- 147254166
- Full Text :
- https://doi.org/10.1016/j.jsc.2020.08.004