Interpolation and Approximation

By P. Revesz. 2010

785 citations recorded by the source corpus.

Subfields: Environmental Engineering, Geology, Pollution

View Paper: https://www.semanticscholar.org/paper/5ed1d6261984992fea16a4a35ec331c0916bdb3c

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Citations in the corpus

Local and global asymptotic inference in smoothing spline models (2012, background): “The reproducing kernel K , if it exists, is uniquely determined by the corresponding RKHS; see [8].”
Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs (2010, methodology): “Following [10] (page 19), we introduce for any s > 1 the ellipse in the complex plane Es := { w + w 2 ; |w| = s}, which has semi-axes of length s+s −1 2 and s−s 2 .”
Identities and generating functions on Chebyshev polynomials (2012, methodology): “2 Generating functions To derive the related generating functions of Chebyshev polynomials of first and second kind [2, 6], we can consider the generating functions of the complex quantity, introduced in (1.”
Approximation of high-dimensional parametric PDEs * (2015, methodology): “We now use the following estimate (see page 313 of [28]) max z∈Et |Qn(z)| ≤ π t t− 1 , (3.”
ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS (2012, background): “Now, from classical approximation theory ([9, 26]) it is well known that, if vn is analytic in Γn, the coefficient vn,pn is exponentially decaying in pn with a certain rate gn, |vn,pn | ≤ c(gn)e−gnpn ; as a consequence we easily obtain a sharp bound on the Legendre coefficients of u,”
Foundations of Signal Processing (2014, methodology): “We also recommend an earlier textbook by Davis [19] for polynomial approximations, including a full proof of the Chebyshev equioscillation theorem, Theorem 6.”
Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs (2015, background): “14) established at the bottom of page 313 in [8].”
Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation (2008, methodology): “As we have already mentioned in the introduction, generalized definitions of Lagrange polynomials exist and are used in approximation theory literature (see [4] and references therein for the multivariate case and [13] for the univariate case).”
Approximating Spectral Densities of Large Matrices (2013, neutral): “See, for example [11], for three-term recurrences for a wide class of such polynomials, e.”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “5), see Davis [133], Eidelheit [160], and Luecking–Rubel [369, Ch.”
Linearization of matrix polynomials expressed in polynomial bases (2008, background): “for n = 1, 2, · · · and j = 0, 1, · · · , n, and have good (uniform) convergence properties to continuous functions on (a, b) (see [8]).”
Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, background): “It asserts that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function [45].”
A displacement‐based finite element formulation for general polyhedra using harmonic shape functions (2014, background): “This result is possibly due to Runge’s phenomenon [31] and the nonpolynomial nature of the shape functions, although more analysis is needed.”