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• W2591579665 abstract "We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on functions is a computationally intensive problem necessary for many practical problems. We analyze a technique called product-convolution expansion: The operator is locally approximated by a convolution, allowing to design fast numerical algorithms based on the fast Fourier transform. We design various types of expansions, provide their explicit rates of approximation and their complexity depending on the time-varying impulse response smoothness. This analysis suggests novel wavelet-based implementations of the method with numerous assets such as optimal approximation rates, low complexity and storage requirements as well as adaptivity to the kernels regularity. The proposed methods are an alternative to more standard procedures such as panel clustering, cross-approximations, wavelet expansions or hierarchical matrices." @default.
• W2591579665 created "2017-03-16" @default.
• W2591579665 creator A5038104386 @default.
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• W2591579665 date "2017-02-27" @default.
• W2591579665 modified "2023-10-10" @default.
• W2591579665 title "Approximation of Integral Operators Using Product-Convolution Expansions" @default.
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• W2591579665 doi "https://doi.org/10.1007/s10851-017-0714-8" @default.
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