Approximating the approximant: A numerical code for polynomial compression of discrete integral operators. 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(n^2)) complexity is shown to be reduced to (O(mn)), with (mll n).
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References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- Sommariva, Alvise: A fast Nyström-Broyden solver by Chebyshev compression (2005)
- Sommariva, Alvise; Vianello, Marco; Zanovello, Renato: Adaptive bivariate Chebyshev approximation (2005)
- De Marchi, Stefano: On Leja sequences: some results and applications (2004)
- De Marchi, Stefano; Vianello, Marco: Approximating the approximant: A numerical code for polynomial compression of discrete integral operators (2001)