Displaying similar documents to “On global smoothness preservation in complex approximation”

Tractability of multivariate problems for weighted spaces of functions

H. Woźniakowski (2006)

Banach Center Publications

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We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.

General uniform approximation theory by multivariate singular integral operators

George A. Anastassiou (2012)

Annales Polonici Mathematici

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We study the uniform approximation properties of general multivariate singular integral operators on ℝ N , N ≥ 1. We establish their convergence to the unit operator with rates. The estimates are pointwise and uniform. The established inequalities involve the multivariate higher order modulus of smoothness. We list the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators to which this theory can be applied directly.

On the Multivariate Robinson-Schensted Correspondence

Fabrizio Caselli (2008)

Bollettino dell'Unione Matematica Italiana

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We show the existence of a multivariate extension of the Robinson-Schensted correspondence. This is inspired by the interpretation of the classical two dimensional case in the invariant theory of (finite) reflection groups.

On the approximation by compositions of fixed multivariate functions with univariate functions

Vugar E. Ismailov (2007)

Studia Mathematica

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The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.

Forecasting time series with multivariate copulas

Clarence Simard, Bruno Rémillard (2015)

Dependence Modeling

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In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our...

Multivariate extensions of expectiles risk measures

Véronique Maume-Deschamps, Didier Rullière, Khalil Said (2017)

Dependence Modeling

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This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

Equivalence Between K-functionals Based on Continuous Linear Transforms

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10. The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes. Partially supported by grant No. 103/2007...