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Hyperbolic Cross Approximation

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Dinh Dũng, "Hyperbolic Cross Approximation"
English | ISBN: 3319922394 | 2018 | 336 pages | PDF | 3 MB

This book gives 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. The multivariate problems turn out to be much more difficult than their univariate counterparts. Recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents results and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many important open problems in the book will provide both students and professionals ideas for further research.

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