Interpolation and Approximation by Polynomials

By George M. Phillips. 2003

669 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5b66030c1f8a665ecd50a1a6f386d2740351714a

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In Applied Mathematics

In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Generalized q-Baskakov operators (2011, background): “q := (q, q)n (q, q)k(q, q)n−k = [n]q! [k]q! [n− k]q! for n ≥ k ≥ 1, and has the value 1 when k = 0 and value zero otherwise (see [26] and [3]).”
Wavelets on Graphs via Spectral Graph Theory (2009, positive): “An overview of Chebyshev polynomial approximation may be found in [50], we recall here briefly a few of their key properties.”
Accelerated filtering on graphs using Lanczos method (2015, methodology): “Theorem 1 shows that the error is bounded by the best polynomial approximation [14] of g on [0 , λ max ] .”
The rate of convergence of q‐Durrmeyer operators for 0 (2008, methodology): “,r and Bn,q(t s; x) is a polynomial of degree min(s,n) (see [4]), we obtain Mn,q(t ; x) is a polynomial of degree min(r,n).”
A high‐order hybridizable discontinuous Galerkin method for elliptic interface problems (2013, background): “It follows from the standard interpolation theory [25] that jg.”
Image denoising with nonlocal spectral graph wavelets (2010, neutral): “, [20] for overview).”
Bernstein series solutions of pantograph equations using polynomial interpolation (2012, background): “[20] Let x and the abscissas x0; x1; .”
On Some Classes of q-parametric Positive linear Operators (2005, methodology): “Phillips [6], [ 7 ] has introduced the q-parametric Bernstein polynomials denoted by Bn(f, x, q), 0 <q ≤ 1. In [6] the investigation of the properties of these polynomials is based on some generalization of divided differences and on the Newton interpolation formula.”