Hyperbolic cross approximation

• 作者： Dung, Dinh, author.
• 其他作者：
  • Temlyakov, Vladimir, author.
  • Ullrich, Tino, author.
  • Tikhonov, Sergey, editor.
  • SpringerLink (Online service)
• 其他題名：
  • Advanced courses in mathematics - CRM Barcelona.
• 出版： Cham : Springer International Publishing :Imprint: Birkhauser
• 叢書名： Advanced courses in mathematics - CRM Barcelona,
• 主題： Approximation theory. , Differential equations, Hyperbolic. , Multivariate analysis. , Approximations and Expansions. , Numerical Analysis.
• ISBN： 9783319922409 (electronic bk.) 、 9783319922393 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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.
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