Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials
نویسندگان
چکیده
منابع مشابه
Numerical and Symbolical Methods Computing the Greatest Common Divisor of Several Polynomials
The computation of the Greatest Common Divisor (GCD) of a set of polynomials is an important issue in computational mathematics and it is linked to Control Theory very strong. In this paper we present different matrix-based methods, which are developed for the efficient computation of the GCD of several polynomials. Some of these methods are naturally developed for dealing with numerical inaccu...
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متن کاملThe Numerical Greatest Common Divisor of Univariate Polynomials
This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in conventional GCD computation is identified by its geometry where polynomials form differentiable manifolds entangled in a stratification structure. With a proper r...
متن کاملComputing the Greatest Common Divisor of Multivariate Polynomials over Finite Fields
Richard Zippel’s sparse modular GCD algorithm is widely used to compute the monic greatest common divisor (GCD) of two multivariate polynomials over Z. In this report, we present how this algorithm can be modified to solve the GCD problem for polynomials over finite fields of small cardinality. When the GCD is not monic, Zippel’s algorithm cannot be applied unless the normalization problem is r...
متن کاملGreatest common divisor
In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), highest common factor (hcf), or greatest commonmeasure (gcm), of two or more integers (when at least one of them is not zero), is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.[1][2] This notion can be extended to polynomials, see ...
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ژورنال
عنوان ژورنال: Special Matrices
سال: 2017
ISSN: 2300-7451
DOI: 10.1515/spma-2017-0015