Results 21 to 30 of about 4,353,527 (290)
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width [PDF]
, 1998 It is known that evaluating the Tutte polynomial, $T(G; x, y)$, of a graph, $G$, is $\#$P-hard at all but eight specific points and one specific curve of the $(x, y)$-plane.
Noble, S D
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A Polynomial Splines Identification Method Based on Control Nets
Complexity, 2020 In this study, based on Polynomial Splines with control nets, an identification method is investigated. We introduce polynomial splines with control nets defined over T-mesh.
Zhihua Wang, Hongmei Kang
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The Computation of Multiple Roots of a Bernstein Basis Polynomial [PDF]
SIAM Journal on Scientific Computing, 2020 This paper describes the algorithms of Musser and Gauss for the computation of multiple roots of a theoretically exact Bernstein basis polynomial $\hat{f}(y)$ when the coefficients of its given form $f(y)$ are corrupted by noise. The exact roots of $f(y)$ can therefore be assumed to be simple, and thus the problem reduces to the calculation of multiple
Martin Bourne +2 more
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Hilbert Basis Theorem and Grobner Basis for Polynomial Ideals [PDF]
, 2020 This paper is an exposition of Hilbert Basis Theorem and Grobner Basis. We first recall some basis concepts of the ideal theory and Hilbert Basis theorem for Polynomial ideals.
Sandar, Lwin Mar Htun
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Spline Approximation, Part 2: From Polynomials in the Monomial Basis to B-splines—A Derivation
Mathematics, 2021 In a series of three articles, spline approximation is presented from a geodetic point of view. In part 1, an introduction to spline approximation of 2D curves was given and the basic methodology of spline approximation was demonstrated using splines ...
Nikolaj Ezhov +2 more
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Intra-Basis Multiplication of Polynomials Given in Various Polynomial Bases
CoRR, 2021 Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In this work, we present formulas and techniques for polynomial multiplications expressed in a variety of well-known ...
S. Karami +3 more
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Egyptian Informatics Journal, 2022 Encryption schemes like AES require finite field modular multiplication. The encryption speed is highly dependent on the performance of the finite field multiplier.
Sakshi Devi, Rita Mahajan, Deepak Bagai
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The Gröbner basis of the ideal of vanishing polynomials
Journal of Symbolic Computation, 2011 We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner basis is independent of the monomial order and that the set of leading terms of the constructed Groebner basis is
Gert-Martin Greuel +2 more
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On computing nullspace bases - a fault detection perspective [PDF]
, 2008 We discuss computationally efficient and numerically reliable algorithms to compute minimal proper nullspace bases of a rational or polynomial matrix.
Andras Varga, Varga, Andreas
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A basis for residual polynomials in 𝑛 variables [PDF]
Transactions of the American Mathematical Society, 1935 Kempnert has established the existence of a basis for residual polynomials in one variable with respect to a composite modulus. A residual polynomial modulo m is by definition a polynomial f(x) with integral coefficients which is divisible by m for every integral value of x, and a residual congruence is written f(x) -(mod n).
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