Numerical Methods for Singularities Via Sinc Functions.
UTAH UNIV SALT LAKE CITY DEPT OF MATHEMATICS
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This paper summarizes the results known to date for using sinc functions composed with other functions as bases for approximations in numerical analysis. Described in this paper are methods of interpolation and approximation of functions and their derivatives, quadrature, the approximate evaluation of transforms Hilbert, Fourier, Laplace, Hankel and Mellin and the approximate solution of differential and integral equations. The methods have many advantages over classical methods which use polynomials as bases. In addition, all of the methods converge at an optimal rate, if singularities on the boundary of approximation are ignored. Author
- Numerical Mathematics