Abstract
Usually, the fast evaluation of a convolution integral f ℝ f(y)g(x−y)dy requires that the functions f, g are discretised on an equidistant grid in order to apply FFT. Here we discuss the efficient performance of the convolution in locally refined grids. More precisely, f and g are assumed to be piecewise linear and the convolution result is projected into the space of linear functions in a given locally refined grid. Under certain conditions, the overall costs are still O(N logN), where N is the sum of the dimensions of the subspaces containing f, g and the resulting function.
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© 2008 Springer-Verlag Berlin Heidelberg
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Hackbusch, W. (2008). Fast Projected Convolution of Piecewise Linear Functions on Non-equidistant Grids. In: Breitner, M.H., Denk, G., Rentrop, P. (eds) From Nano to Space. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74238-8_12
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DOI: https://doi.org/10.1007/978-3-540-74238-8_12
Publisher Name: Springer, Berlin, Heidelberg
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