A new multiquadric quasi‐interpolation operator with interpolation property
Mathematical Methods in the Applied Sciences, 2013In this article, we discuss a class of multiquadric quasi‐interpolation operator that is primarily on the basis of Wu–Schaback's quasi‐interpolation operator and radial basis function interpolation. The proposed operator possesses the advantages of linear polynomial reproducing property, interpolation property, and high accuracy.
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Quasi-interpolation operators based on a cubic spline and applications in SAMR simulations
Applied Mathematics and Computation, 2010The authors construct a certain compactly supported univariate \(C^2\) cubic spline function and its tensor-product bivariate extension. The theoretical and numerical results presented show that the discrete convolution operators based on these two functions are monotonic and conservative.
Libin Ma, Zeyao Mo, Xiaowen Xu
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A Complete Asymptotic Expansion for the Quasi-interpolants of Gauß–Weierstraß Operators
Mediterranean Journal of Mathematics, 2018We derive the complete asymptotic expansion for the quasi-interpolants of Gaus–Weierstras operators $$W_{n}$$ and their left quasi-interpolants
Ulrich Abel +2 more
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Durrmeyer Operators and Their Natural Quasi-Interpolants
2006Abstract This paper provides a survey on spectral analysis and approximation order of our quasi-interpolants of Durrmeyer type on simplices, together with various new aspects and achievements. The latter include Bernstein type inequalities which are proved using a striking property of appropriately modified Durrmeyer operators, namely, their kernel
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Bernstein–Bézier representation and near-minimally normed discrete quasi-interpolation operators
Applied Numerical Mathematics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barrera-Rosillo, Domingo +1 more
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Representation of quasi-interpolants as differential operators and applications
1999Most of the best known positive linear operators are isomorphisms of the maximal subspace of polynomials that they preserve. We give here the differential forms of these isomorphisms and of their inverses for Bernstein and Szasz-Mirakyan operators, and their Durrmeyer and Kantorovitch extensions.
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The Complete Asymptotic Expansion for the Left Quasi Interpolants of Müller's Gamma Operators
Numerical Functional Analysis and Optimization, 2003Abstract Recently, Muller introduced and studied left quasi interpolants of his Gamma operators. In this article we present the complete asymptotic expansion of these operators. As a special case we obtain a Voronovskaja type theorem.
Ulrich Abel, Mircea Ivan
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Approximation by a Kantorovich–Shilkret Quasi-interpolation Neural Network Operator
2018In this chapter we present multivariate basic approximation by a Kantorovich–Shilkret type quasi-interpolation neural network operator with respect to supremum norm. This is done with rates using the multivariate modulus of continuity. We approximate continuous and bounded functions on \( \mathbb {R}^{N}\), \(N\in \mathbb {N}\).
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A new multiquadric quasi‐interpolation operator with interpolation property
Mathematical Methods in the Applied Sciences, 2014Jinming Wu
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An iterated quasi-interpolation approach for derivative approximation
Numerical Algorithms, 2020Zhengjie Sun, Zongmin Wu, Wenwu Gao
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