Approximating the Approximant: A Numerical Code for Polynomial Compression of Discrete Integral Operators |
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Authors: | Stefano De Marchi Marco Vianello |
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Affiliation: | (1) Dipartimento di Informatica, University of Verona, Italy;(2) Dipartimento di Matematica Pura e Applicata, University of Padova, Italy |
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Abstract: | The action of various one-dimensional integral operators, discretized by a suitable quadrature method, can be compressed and accelerated by means of Chebyshev series approximation. Our approach has a different conception with respect to other well-known fast methods: its effectiveness rests on the smoothing effect of integration, and it works in linear as well as nonlinear instances, with both smooth and nonsmooth kernels. We describe a Matlab toolbox which implements Chebyshev-like compression of discrete integral operators, and we present several numerical tests, where the basic O(n2) complexity is shown to be reduced to O(mn), with mn. |
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Keywords: | linear and nonlinear discrete integral operators Chebyshev series expansion compression fast evaluation |
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