Abstract
We study approximation problems for infinitely differentiable multivariate functions in the worst-case setting. Using a series of information-based algorithms as approximation tools, in which each algorithm is constructed by performing finitely many standard information operations, we prove that the L∞-approximation problem is exponentially convergent. As a corollary, we show that the corresponding integral problem is exponentially convergent as well.
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Liu, Y., Xu, G. & Zhang, J. Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions. Math Notes 103, 769–779 (2018). https://doi.org/10.1134/S0001434618050097
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DOI: https://doi.org/10.1134/S0001434618050097