منابع مشابه
Certiied Approximate Univariate Gcds
We study the approximate GCD of two univariate polynomials given with limited accuracy or, equivalently, the exact GCD of the perturbed polynomials within some prescribed tolerance. A perturbed polynomial is regarded as a family of polynomials in a clas-siication space, which leads to an accurate analysis of the computation. Considering only the Sylvester matrix singular values, as is frequentl...
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We compare the two main competing methods for fast univariate polynomial GCD computation over an algebraic number field, namely, the modular method of Langymyr et al (1987), and the heuristic method of Smedley et al (1988). Because of recent improvements to the modular method by Encarnacion (1994), we expected that the modular method, if implemented “properly”, would now be the method of choice...
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The pejorative manifold was defined by Kahan in 1972. While multiple roots of a polynomial are naturally ill conditioned, we have that: if we know the multiplicities of the roots, then the roots are well conditioned. Consider a polynomial p with k distinct roots zi, the ith root has multiplicity mi, for i = 1, 2, . . . , k. The degree n of p is then the sum of multiplicities: n = m1 +m2 + · · ·...
متن کاملApproximate GCDs of polynomials and sparse SOS relaxations
The problem of computing approximate GCDs of several polynomials with real or complex coefficients can be formulated as computing the minimal perturbation such that the perturbed polynomials have an exact GCD of given degree. We present algorithms based on SOS (Sum of Squares) relaxations for solving the involved polynomial or rational function optimization problems with or without constraints.
متن کاملA geometrical approach to finding multivariate approximate LCMs and GCDs
In this article we present a new approach to compute an approximate least common multiple (LCM) and an approximate greatest common divisor (GCD) of two multivariate polynomials. This approach uses the geometrical notion of principal angles whereas the main computational tools are the Implicitly Restarted Arnoldi Method and sparse QR decomposition. Upper and lower bounds are derived for the larg...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1997
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00013-3