Approximation of functions with bounded mixed derivative

By V. N. Temli︠a︡kov. 1989

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Approximation rates for the hierarchical tensor format in periodic Sobolev spaces (2014, background): “These definitions are analogous to those in Temlyakov’s monograph [44].”
Sparse finite element approximation of high-dimensional transport-dominated diffusion problems (2008, background): “traced back to the works of Babenko [2] and Smolyak [26]; we refer to the papers of Temlyakov [ 29 ], DeVore, Konyagin & Temlyakov [8] for the study of high-dimensional approximation problems, to the works of Wasilkowski & Wo´zniakowski [30] and Novak & Ritter [19] for high-dimensional integration p”
On the Small Ball Inequality in All Dimensions (2007, unknown): “See (Fefferman and Pipher, 1997; Wang, 1991).”
Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems (2005, background): “[25, 13]) allows to get rid of this phenomenon.”
Greedy approximation (2008, background): “(1.9.3) The following nonlinear analogues of the Kolmogorov widths and the ortho-widths (see, for instance, Temlyakov (1989a)) were considered in Temlyakov (2000a, 2002a, 2003a).”
Optimized Tensor-Product Approximation Spaces (2000, methodology): “The sparse grid scheme is well established in approximation and interpolation theory [Bab60], [BDJ92], [Del82], [Go69], [Sm63], [Te93], [ Te89 ], [WW95].”
Approximation characteristics of the classes Bp,θΩ of periodic functions of many variables (2006, background): “For example, quantities (14) and (15) for the classes of functions of many variables W r p,α and H r p were investigated in [7, 8 ]. The investigation of the orthoprojector widths of the classes of functions of many variables B r was carried out in [9, 10], where one can also find a detailed biblio”
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators (2005, background): “Alternative ideas based on sparse grid finite elements/wavelets have been successfully applied [3], [18], [12], [19].”
Hyperbolic Cross Approximation (2016, methodology): “The reader can find a discussion of related questions in [345], Chapter 2, Section 5.”
Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, background): “Eine solche findet sich offenbar zuerst bei Miroshin u. Khromov [70], welche für g ∈ Hs([0,1]2) (s ganzzahlig) zeigen, dass inf f ∈C≤r,2 ‖ f −g‖0. r−s. Das Ergebnis wurde von Temlyakov [96, 99, 100] auf den periodischen Fall und m1,m2 ≥ 1 zu inf f ∈C≤r,2 ‖ f −g‖0 ∼ r−s/min(m1,m2) für g ∈ Bs2π, sowie”