منابع مشابه
Approximate GCD of Multivariate Polynomials
Given two polynomials F and G in R[x1, . . . , xn], we are going to find the nontrivial approximate GCD C and polynomials F , G ∈ R[x1, . . . , xn] such that ||F − CF ′|| < and ||G − CG′|| < , for some and some well defined norm. Many papers 1,2,3,5,8,10,11,13,15 have already discussed the problem in the case n = 1. Few of them 2,10,11 mentioned the case n > 1. Approximate GCD computation of un...
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We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]/(f). In particular, the structure of the null space of the multiplicat...
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− The problem of finding the greatest common divisor (GCD) of univariate polynomials appears in many engineering fields. Despite its formulation is well-known, it is an ill-posed problem that entails numerous difficulties when the coefficients of the polynomials are not known with total accuracy, as, for example, when they come from measurement data. In this work we propose a novel GCD estimati...
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Abstract — In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given. 2000 Mathematics Sub...
متن کاملDual generalized Bernstein basis
The generalized Bernstein basis in the space Πn of polynomials of degree at most n, being an extension of the q-Bernstein basis introduced recently by G.M. Phillips, is given by the formula (see S. Lewanowicz & P. Woźny, BIT 44 (2004), 63–78) Bn i (x;ω| q) := 1 (ω; q)n [ n i ] q x (ωx−1; q)i (x; q)n−i (i = 0, 1, . . . , n). We give explicitly the dual basis functions Dn k (x; a, b, ω| q) for th...
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ژورنال
عنوان ژورنال: ACM Communications in Computer Algebra
سال: 2019
ISSN: 1932-2240
DOI: 10.1145/3377006.3377011