Positive Approximation and Interpolation Using Compactly Supported Radial Basis Functions
TL;DR: In this paper, the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity, is discussed.
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Abstract: We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the proposed method is flexible.
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Citations
On a class of non-stationary, compactly supported spatial covariance functions
TL;DR: A new class of non-stationary, compactly supported spatial covariance functions is presented, which adapts a class of convolution-based flexible models to non- stationary situations.
20
Shape-Preservation of the Four-Point Ternary Interpolating Non-stationary Subdivision Scheme
TL;DR: In this paper, the shape-preserving properties of the four-point ternary non-stationary interpolating subdivision scheme (the fourpoint scheme) were analyzed and the conditions on the tension parameter and initial control polygon that permit the creation of positivity and monotonicity preserving curves after a finite number of subdivision steps were derived.
17
Positive constrained approximation via RBF-based partition of unity method
TL;DR: In this article, Wu et al. discuss the problem of constructing Radial Basis Function (RBF)-based Partition of Unity (PU) interpolants that are positive if data values are positive.
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Positivity Preserving Interpolation Using Rational Bicubic Spline
TL;DR: This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases and its partially blended rational bicubic spline is on a par with the established methods.
References
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
TL;DR: A new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support is constructed, it is proved that they are of minimal degree and unique up to a constant factor.
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Radial Basis Functions: Theory and Implementations
Martin D. Buhmann
- 07 Jul 2003
TL;DR: In this paper, a radial basis function approximation on infinite grids is proposed, based on the wavelet method with radial basis functions (WBFF) with compact support, which is a general method for approximation and interpolation.
Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
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Radial basis functions for multivariable interpolation: a review
M. J. D. Powell
- 01 Jan 1987
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Mathematical Methods for Curves and Surfaces
Michael S. Floater,Tom Lyche,Marie-Laurence Mazure,Knut Mørken,Larry L. Schumaker +4 more
- 01 Jan 2010
TL;DR: A construction of rational isotropic curves with a prescribed tangent field which leads to the description of all rational minimal surfaces is presented.
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