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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 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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New Algorithm for Computing the Hermite Interpolation Polynomial
Numerical Algorithms, 2018Hassane Sadok
exaly
Inversion of Polynomial Matrices by Interpolation
IEEE Transactions on Automatic Control, 1992P Hippe
exaly
GRPIA: A New Algorithm for Computing Interpolation Polynomials
Numerical Algorithms, 2019Hassane Sadok
exaly
Kötter Interpolation in Skew Polynomial Rings
Designs, Codes, and Cryptography, 2014Frank Kschischang, Felice Manganiello
exaly

