Results 261 to 270 of about 4,353,527 (290)

Gröbner Basis Methods in Polynomial Modelling

1998
The Grobner basis (G-basis) method in the design of experiments was introduced by Pistone & Wynn (1996) and followed up by several strands of work one in particular addressing real practical applications: Holliday, Pistone, Riccomagno & Wynn (1997). This paper continues this latter series.
R. A. BATES, B. GIGLIO, RICCOMAGNO, EVA, H. P. WYNN   +3 more
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Birkhoff Polynomial Basis

2017
The Birkhoff interpolation problem is an extension of the well-known Lagrange and Hermite interpolation problems. We propose a new set of basis polynomials for representing the Birkhoff interpolation polynomial . The proposed basis extends the definition of the Newton basis for non-distinct interpolation nodes.
Amir Amiraslani, Heike Faßbender, Nikta Shayanfar   +2 more
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Polynomial-Basis Arithmetic

2020
This chapter is on arithmetic and related operations over the field GF(2m) with polynomial-basis representations. The first section is on addition, subtraction, multiplication, and squaring; although subtraction is just an instance of addition, optimal squaring is not just multiplication with the same operand. The second section is on reduction.
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Change of Basis for Products of Orthogonal Polynomials

SIAM Journal on Algebraic Discrete Methods, 1987
Given two sets of orthogonal polynomials $\mathcal{B} = \{ p_i (\lambda )\} $ and $\{ q_i (\lambda )\} $, simple procedures are given for expressing the products $\lambda ^i p_j (\lambda ),\lambda ^i q_j (\lambda ),p_i (\lambda )q_j (\lambda )$ and $q_i (\lambda )q_j (\lambda )$ in terms of the basis $\mathcal{B}$.
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Surface Reconstruction and Lagrange Basis Polynomials

2008
Surface reconstruction, based on line integrals along segments of the unit disk is studied. Various methods concerning with this problem are known. We consider here interpolation over regular schemes of chords by polynomials. We find the interpolant in Lagrange form and investigate some properties of Lagrange basis polynomials.
Irina Georgieva, Rumen Uluchev
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The symmetric analogue of the polynomial power basis

ACM Transactions on Graphics, 1997
A new polynomial basis over the unit interval t∈[0,1] is proposed. The work is motivation by the fact that the monomial (power) form is not suitable in CAGD, as it suffers from serious numerical problems, and the monomial coefficients have no geometric meaning.
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Groebner Basis for Polynomials with Parametric Exponents

2008 International Conference on Computational Sciences and Its Applications, 2008
For some classes of singularities there exist defining equations with parametric coefficients and exponents. We can treat these defining equation with parametric exponents as sequences and calculate their Grobner bases. Grobner bases are useful for clarifying the structure of the parameters of the defining equation, which will enable us to discover ...
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The Condition of the B-Spline Basis for Polynomials

SIAM Journal on Numerical Analysis, 1988
It is shown that the polynomial basis provided on a knot by the kth order B-splines which do not vanish on that interval is well conditioned up to a scaling exactly to the extent that at least $k -1$ of the knots stay finite relative to the length of that knot interval.
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A basis theorem for polynomial modules

Mathematical Proceedings of the Cambridge Philosophical Society, 1956
The purpose of the present note is to prove a basis theorem for polynomial modules (Theorem 1 below). As an application, a proof of the Hilbert function theorem for homogeneous modules (Snapper (1)) is obtained. Both these proofs are elementary in the sense that they do not depend on the decomposition theory for modules over a Noether ring.
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Chebyshev Polynomials as Basis Functions

2018
In the present chapter some of the important properties of Chebyshev polynomials are described, including their recursion relations, their analytic expressions in terms of the powers of the variable x, where \( -1\le x\le 1\), and the mesh points required for the Gauss–Chebyshev integration expression described in Chap. 3.
George Rawitscher, Victo dos Santos Filho, Thiago Carvalho Peixoto   +2 more
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