Note on "The smoothing effect of integration in ℝd and the ANOVA decomposition"
Mathematics of Computation, 2012 This paper studies the ANOVA decomposition of a d-variate function f dened on the whole of R d , where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function).
M. Griebel, F. Kuo, I. Sloan
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Inequalities for a class of multivariate operators
Journal of Inequalities and Applications, 2012 This paper introduces and studies a class of generalized multivariate Bernstein operators defined on the simplex. By means of the modulus of continuity and so-called Ditzian-Totik’s modulus of function, the direct and inverse inequalities for the ...
Jian-wei Zhao
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Weighted Integral of Infinitely Differentiable Multivariate Functions is Exponentially Convergent
Numerical Mathematics: Theory, Methods and Applications, 2019 We study the problem of a weighted integral of infinitely differentiable multivariate functions defined on the unit cube with the L∞-norm of partial derivative of all orders bounded by 1.
Guiqiao Xu
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Strictly positive definite kernels on compact two-point homogeneous spaces
, 2016 We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a compact two-point homogeneous space. The characterization is achieved using special limit formulas for
V. S. Barbosa, V. Menegatto
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On Whitney type inequalities for local anisotropic polynomial approximation [PDF]
, 2010 We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in $L_p(Q)$ with $1\leq p\leq \infty$. Here $Q$ is a $d$-parallelepiped in $\RR^d$ with sides parallel to the coordinate axes.
Dinh, D., Ullrich, T.
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Low cardinality admissible meshes on quadrangles, triangles and disks
, 2012 Using classical univariate polynomial inequalities (Ehlich and Zeller, 1964), we show that there exist admissible meshes with O(n2) points for total degree bivariate polynomials of degree n on convex quadrangles, triangles and disks.
Len Bos, M. Vianello
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Approximations by multivariate sublinear and Max-product operators under convexity
Demonstratio Mathematica, 2018 Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators.
Anastassiou George A.
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Lagrange interpolation at real projections of Leja sequences for the unit disk [PDF]
, 2011 We show that the Lebesgue constant of the real projection of Leja sequences for the unit disk grows like a polynomial. The main application is the first construction of explicit multivariate interpolation points in $[-1,1]^N$ whose Lebesgue constant also
Alper +13 more
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Best N-term approximation in electronic structure calculations. II. Jastrow factors
, 2007 We present a novel application of best N-term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction.
H. Flad, W. Hackbusch, R. Schneider
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Numerical hyperinterpolation over nonstandard planar regions [PDF]
, 2017 We discuss an algorithm (implemented in Matlab) that computes numerically total-degree bivariate orthogonal polynomials (OPs) given an algebraic cubature formula with positive weights, and constructs the orthogonal projection (hyperinterpolation) of a ...
Sommariva, Alvise, Vianello, Marco
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