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Note on Polynomial Interpolation [PDF]
Mathematical Notes, 1932 The formulae of interpolation of Lagrange and Newton are easily retained in the memory if one considers a simple way in which each can be derived, for polynomials.
A. C. Aitken
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On the Hermite interpolation polynomial
Journal of Approximation Theory, 1984 An elementary inductive proof of the Hermite interpolation polynomial is presented. The proof is constructive, i.e., it gives a method for determining the interpolation polynomial. A numerical example is given.
Hannu Väliaho
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On monotone polynomial interpolation [PDF]
Mathematica Moravica, 2001 The author gives a new proof of \textit{W. Wolibner}'s famous theorem of monotone polynomial interpolation [Colloq. Math. 2, 136-137 (1951; Zbl 0043.01904)] and proposes a strategy that allows to reduce the degree of the polynomial.
Nicolae Todor
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Interpolation by non-negative polynomials
Journal of Approximation Theory, 1980 It is an elementary fact that given any continuous real function f on 10, 1 1 and any n + 1 points on its graph, there exists a unique polynomial p, of degree
John T. F. Briggs, Lee A. Rubel
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On partial polynomial interpolation [PDF]
Linear Algebra and its Applications, 2011 34 pages, 2 tables, revised version: different proof of Theorem 4.1, Section 4 significantly changed, Appendix ...
C. Brambilla, OTTAVIANI, GIORGIO MARIA
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Interpolation with the polynomial kernels
, 2022 The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness.
Elefante G. +5 more
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Approximation by interpolating polynomials
Journal of Approximation Theory, 1978 AbstractThe problem of convergence of interpolating polynomials of the type ln(x,f)=a(n)02+∑k=1n(a(n)k cos kt + b(n)k sin kt) with the interpolating points tj(n) = 2πj(2n + 1) has been studied by A. Zygmund, who considered the partial sums of the interpolating polynomials In,v(x, f). On the other hand, R.
A.S.B Holland, B Kuttner, B.N Sahney
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Complex Interpolating Polynomials [PDF]
Proceedings of the American Mathematical Society, 1988 Let I n , m ( f , z ) {I_{n,m}}\left ( {f,z} \right ) be the unique interpolatory polynomial of degree ≤ 2 n − 1
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Tricubic Polynomial Interpolation [PDF]
Proceedings of the National Academy of Sciences, 1971 A new triangular “finite element“ is described; it involves the 12-parameter family of all quartic polynomial functions that are “tricubic“ in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a ...
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On the divergence of polynomial interpolation
Journal of Approximation Theory, 2003 The authors consider a triangular interpolation scheme on a continuous piecewise \(C^1\) curve of the complex plane and denote the closure of this triangular scheme by \(\Gamma\). Given a meromorphic function \(f\) with no singularity on \(\Gamma\) they examine the region of convergence of the sequence of interpolating polynomials to the function \(f\).
Àngel Jorba, Joan Carles Tatjer
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