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Interpolation with symmetric polynomials
Numerical Algorithms, 2016Interpolation problems in more than one dimensional ambient spaces are studied in this article. Whenever the dimension of the ambient space is more than one, these problems are a lot more difficult to analyse than the classical univariate problems, for instance because not only convergence properties but also existence questions of interpolants ...
Jesús M. Carnicer, Carmen Godés
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Journal of Computational and Applied Mathematics, 2020
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Abderrahim Messaoudi +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abderrahim Messaoudi +2 more
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A Note on Polynomial Interpolation
International Journal of Computer Mathematics, 2002The Neville's algorithm and the Aitken's algorithm are successively linear interpolation approach to high degree Lagrangian interpolation. This note proposes a new approach with iteratively quadratic interpolation to high degree Lagrangian interpolation. The new algorithm here is cheaper (about 20% cheaper) than the Neville's algorithm.
Waléria Adriana Gonçalez Cecilio +5 more
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Interpolating polynomial wavelets on [?1,1]
Advances in Computational Mathematics, 2004The authors use a system of orthogonal polynomials with respect to the four Chebyshev weights, \(1/\sqrt(1-x^2)\), \(\sqrt(1-x^2)\), \(\sqrt{[(1-x)/(1+x)]}\) and \(\sqrt{[(1+x)/(1-x)]}\), with positive leading coefficients and Darboux kernels to construct four interpolating scaling functions and interpolating wavelets with a multiresolution structure ...
Capobianco MR, Themistoclakis W
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Polynomial Interpolation on the Unit Sphere
SIAM Journal on Numerical Analysis, 2003The main result of the paper provides families of points on the unit sphere in \(\mathbb R^3\), which admit unique solution to the problem of interpolation at these points by spherical polynomials of 3 variables of any given degree [cf. \textit{B. Bojanov} and \textit{Y. Xu}, SIAM J. Numer. Anal. 39, 1780--1793 (2002; Zbl 1014.41002)].
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Polynomial Interpolation of the Discrete Logarithm
Designs, Codes and Cryptography, 2002The paper provides lower bounds on the degree and the sparsity of polynomials interpolating the discrete logarithm in a finite field. The results extend the work of \textit{D. Coppersmith} and \textit{I. E. Shparlinski} [J. Cryptology 13, 339-360 (2000; Zbl 1038.94007)] from finite prime fields to arbitrary finite fields.
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2018
Corollary 15.10 assures that there is at most one polynomial of degree n and assuming preassigned values in n + 1 given complex numbers. What we still do not know is whether such a polynomial actually exists. For instance, does there exists a polynomial f with rational coefficients, degree 3 and such that f(0) = 1, f(1) = 2, f(2) = 3 and f(3) = 0?
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Corollary 15.10 assures that there is at most one polynomial of degree n and assuming preassigned values in n + 1 given complex numbers. What we still do not know is whether such a polynomial actually exists. For instance, does there exists a polynomial f with rational coefficients, degree 3 and such that f(0) = 1, f(1) = 2, f(2) = 3 and f(3) = 0?
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Summability of Interpolating Polynomials
Journal of the London Mathematical Society, 1980Kuttner, Brian, Sahney, B.
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Polynomial evaluation and interpolation on special sets of points
Journal of Complexity, 2005Alin Boštan, Eric Schost
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