Stephan Dahlke, Marc Hovemann, Thorsten Raasch, Dorian Vogel
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引用次数: 0
Abstract
This paper is concerned with near-optimal approximation of a given univariate function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by hp-approximation techniques of Binev, we use the underlying tree structure of the frame elements to derive an adaptive algorithm that, under standard assumptions concerning the local errors, can be used to create approximations with an error close to the best tree approximation error for a given cardinality. We support our findings by numerical experiments demonstrating that this approach can be used to achieve inverse-exponential convergence rates.
本文涉及用多项式丰富小波框架（即所谓的夸克框架）的元素对给定的单变量函数进行近优逼近。受 Binev 的 hp 近似技术启发，我们利用框架元素的底层树形结构推导出一种自适应算法，在有关局部误差的标准假设下，该算法可用于创建误差接近给定心率的最佳树形近似误差的近似值。我们通过数值实验证明，这种方法可以达到反指数收敛率，从而支持我们的研究结果。
期刊介绍：
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.
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