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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Introduction
verfasst von : Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
Erschienen in: Hyperbolic Cross Approximation
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This book is a survey on multivariate approximation. The 20th century was a period of transition from univariate problems to multivariate problems in a number of areas of mathematics. For instance, it is a step from Gaussian sums to Weil’s sums in number theory, a step from ordinary differential equations to PDEs, a step from univariate trigonometric series to multivariate trigonometric series in harmonic analysis, a step from quadrature formulas to cubature formulas in numerical integration, a step from univariate function classes to multivariate function classes in approximation theory. In many cases this step brought not only new phenomena but also required new techniques to handle the corresponding multivariate problems. In some cases even a formulation of a multivariate problem requires a nontrivial modification of a univariate problem.