An extra-components method for evaluating fast matrix-vector multiplication with special functions
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In calculating integral or discrete transforms, fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, spherical, etc.) functions are often used. The currently available fast algorithms are several orders of magnitude less efficient than the fast Fourier transform. To achieve higher efficiency, a convenient general approach for calculating matrix-vector products for a class of problems is proposed. A series of fast simple-structure algorithms developed under this approach can be efficiently implemented with software based on modern microprocessors. The results of computational experiments show that these procedures can decrease the calculation time by several orders of magnitude compared with the conventional direct method of vector-matrix multiplication.
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