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Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness

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Abstract

We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.

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Acknowledgements

A part of this work was done when the author was working at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and working condition. He expresses thanks to Dr. David Krieg for pointing out the papers [33] and [8] and for useful comments related to these papers.

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  1. Information Technology Institute, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Dinh Dũng

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  1. Dinh Dũng
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Correspondence to Dinh Dũng.

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Dedicated to Professor Ngo Viet Trung.

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Dũng, D. Sparse-grid Sampling Recovery and Numerical Integration of Functions Having Mixed Smoothness. Acta Math Vietnam (2024). https://doi.org/10.1007/s40306-024-00527-7

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