Hyperbolic Cross Approximation

Beschreibung

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.

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.

Autor*in

Dinh Dũng

Themen in »Hyperbolic Cross Approximation«

hyperbolic cross sparse grid mixed smoothness trigonometric polynomial linear approximation Kolmogorov width linear width orthowidth sampling recovery sampling width nonlinear approximation entropy number best m-term approximation numerical integration cubature formulas

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