Approximate square-free part and decomposition. (May 2021)

• Record Type: Journal Article
• Authors: Nagasaka, Kosaku
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 402
• Page End: 418
• Publication Date: 2021-05
• Subjects: Symbolic-numeric algorithm for polynomials -- Approximate polynomial GCD; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.08.004
• Languages: English
• ISSNs: 0747-7171

Abstract

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.