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Numerical differentiation on scattered data through multivariate polynomial interpolation [PDF]
BIT Numerical Mathematics, 2021 We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis.
F. Dell’Accio +3 more
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On multivariate polynomial interpolation [PDF]
Constructive Approximation, 1990 We provide a map which associates each finite set Θ in complexs-space with a polynomial space πΘ from which interpolation to arbitrary data given at the points in Θ is possible and uniquely so. Among all polynomial spacesQ from which interpolation at Θ is uniquely possible, our πΘ is of smallest degree. It is alsoD- and scale-invariant.
Carl de Boor, Amos Ron
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Interpolation by Multivariate Splines [PDF]
Mathematics of Computation, 1988 A general interpolation scheme by multivariate splines at regular sample points is introduced. This scheme guarantees the local optimal order of approximation to sufficiently smooth data functions. A discussion on numerical implementation is included.
Charles K. Chui +2 more
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Electronic Transactions on Numerical Analysis, 2022 . In the classical (non-fractal) setting, the natural kinship between theories of interpolation and approximation is well explored. In contrast to this, in the context of fractal interpolation, the interrelation between interpolation and approximation is
K. K. Pandey, P. Viswanathan
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Polyharmonic splines generated by multivariate smooth interpolation
Computers and Mathematics with Applications, 2019 K. Segeth
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On the history of multivariate polynomial interpolation
Journal of Computational and Applied Mathematics, 2000 AbstractMultivariate polynomial interpolation is a basic and fundamental subject in Approximation Theory and Numerical Analysis, which has received and continues receiving not deep but constant attention. In this short survey, we review its development in the first 75 years of this century, including a pioneering paper by Kronecker in the 19th century.
M. Gasca, Thomas Sauer
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Journal of Water and Climate Change, 2022 In the topographic complex catchments, landscape features have a significant impact on the spatial prediction of rainfall and temperature. In this study, performance assessments were made of various interpolation techniques for the prediction of the ...
Hirpo Gudeta Bati +2 more
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Remote Sensing, 2023 The inclusion of physiographic and atmospheric influences is critical for spatial modeling of orographic precipitation in complex terrains. However, attempts to incorporate cloud cover frequency (CCF) data when interpolating precipitation are limited ...
Karam Alsafadi +6 more
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Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials [PDF]
Foundations of Computational Mathematics, 2020 Sparse interpolation refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations.
E. Hubert, M. Singer
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On Multivariate Interpolation [PDF]
Studies in Applied Mathematics, 2005 A new approach to interpolation theory for functions of several variables is proposed. We develop a multivariate divided difference calculus based on the theory of noncommutative quasi‐determinants. In addition, intriguing explicit formulae that connect the classical finite difference interpolation coefficients for univariate curves with multivariate ...
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