Nonlinear approximation in bounded orthonormal product bases

نویسندگان

چکیده

Abstract We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect suitable truncation basis expansion function, where corresponding support assumed be unknown. method based on point evaluations considered function and adaptively builds index set such that approximately largest coefficients are still included. For this purpose, only needs search space contains desired set. Throughout work, there various minor modifications discussed as well, which may yield additional benefits several situations. first time, we provide proof detection guarantee case under certain assumptions sub-methods used within our algorithm, can foundation similar statements other situations well. Some numerical examples different settings underline effectiveness accuracy method.

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ژورنال

عنوان ژورنال: Sampling theory, signal processing, and data analysis

سال: 2023

ISSN: ['2730-5724', '1530-6429', '2730-5716']

DOI: https://doi.org/10.1007/s43670-023-00057-7