We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained simplest ones based on polynomial, piecewise linear or specific cubic in...

The DE-Sinc formulas, resulting from a combination of the Sinc approximation formula with the double exponential (DE) transformation, provide a highly efficient method for function approximation. In many cases they are more efficient than the SE-Sinc formulas, which are the Sinc approximation formulas combined with the single exponential (SE) transformations. Function classes suited to the SE-S...

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and Sinc-Gaussian based method. The two last Sinc related are exact transforms which allow us numerical approximation using methods. transform converges exponentially does not use Bromwich contours for computations. apply the to Mittag-Leffler functions incorporating one, two, parameters. par...

ÐWe present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients ar...