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Titlebook: Numerical Methods in Approximation Theory, Vol. 9; Dietrich Braess,Larry L. Schumaker (Stevenson Prof Book 1992 Springer Basel AG 1992 Inv

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A Multi-Parameter Method for Nonlinear Least-Squares Approximation,t minimizes each .. separately, and then applies a penalty strategy to gradually force the different minimizers to coalesce. Though the auxiliary nonlinear least-squares method works on ℝ., it is shown that the additional computational requirements consist of . − 1 gradient evaluations plus .(. · .)
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Analog VLSI Networks,al network computation by the analog VLSI implementation technology, an analog model of the first stages of retinal processing has been constructed on a single silicon chip by CMOS VLSI circuitry and applied to machine vision. The purpose of this paper is to study the exactly solvable hexagonal resi
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Converse Theorems for Approximation on Discrete Sets II, consider approximation in the .. norm (. ∈ [1,+∞)) by polynomials, trigonometric polynomials and entire functions of exponential type. We extend some of the known results to approximation on a sequence of discrete sets instead of an interval. The main tools are upper estimates of an .. norm in term
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Blending Approximations with Sine Functions,We show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor product approach but with a reduced number of terms. An example is given which shows that the asymptotic error (when the number of points increases) is exactly of the stated order.
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Estimating the Condition Number for Multivariate Interpolation Problems,nd is based on properties of the symbol of . (which is a periodization of ..). For scattered data interpolation, we assume that . is a positive definite function where the Fourier transform can be properly bounded. As examples, we consider interpolation by box splines or by certain radial basis functions.
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