03175nam 22005775 450 991030011650332120250609111402.03-319-92240-810.1007/978-3-319-92240-9(CKB)4100000007110778(DE-He213)978-3-319-92240-9(MiAaPQ)EBC6315607(PPN)232471150(MiAaPQ)EBC6282304(EXLCZ)99410000000711077820181102d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierHyperbolic Cross Approximation /by Dinh Dũng, Vladimir Temlyakov, Tino Ullrich ; edited by Sergey Tikhonov1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (XI, 218 p. 24 illus., 11 illus. in color.) Advanced Courses in Mathematics - CRM Barcelona,2297-03043-319-92239-4 Includes bibliographical references and index.Introduction -- Trigonometric polynomials -- Function spaces on T^d -- Linear approximation -- Sampling recovery -- Entropy numbers -- Best m-term approximation -- Numerical integration -- Related problems -- High-dimensional approximation -- Appendix.This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.Advanced Courses in Mathematics - CRM Barcelona,2297-0304Approximation theoryNumerical analysisApproximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Approximation theory.Numerical analysis.Approximations and Expansions.Numerical Analysis.511.4Dũng Dinhauthttp://id.loc.gov/vocabulary/relators/aut768267Temlyakov Vladimirauthttp://id.loc.gov/vocabulary/relators/autUllrich Tinoauthttp://id.loc.gov/vocabulary/relators/autTikhonov Sergeyedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910300116503321Hyperbolic Cross Approximation2266034UNINA