Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions |
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Authors: | Yongping Liu Guiqiao Xu Jie Zhang |
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Institution: | 1.School of Mathematical Sciences,Beijing Normal University,Beijing,People’s Republic of China;2.School of Mathematical Sciences,Tianjin Normal University,Tianjin,People’s Republic of China |
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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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