Evaluation of Fourier integrals using $B$-splines

Evaluation of Fourier Integrals Using ß-Splines

Finite Fourier integrals of functions possessing jumps in value, in the first or in the second derivative, are shown to be evaluated more efficiently, and more accurately, using a continuous Fourier transform (CFT) method than the discrete transform method used by the fast Fourier transform (FFT) algorithm. A ß-spline fit is made to the input function, and the Fourier transform of the set of B-...

Moments and Fourier transforms of B-splines

The problem o f determining the moments and the Fourier transforms o f B-splines with arbitrary knots is considered. There exists a simple connect ion between the moments o f such splines and the so-called extended Stirling numbers o f the second kind which are defined in section 2. Some recurrence relations for the moments o f B-splines with arbitrary knots are given in section 3. In the case ...

Numerical solution of functional integral equations by using B-splines

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

Weighted Integrals of Polynomial Splines

The construction of weighted splines by knot insertion techniques such as deBoor and Oslo type algorithms leads immediately to the problem of evaluating integrals of polynomial splines with respect to the positive measure possessing piecewise constant density. It is for such purposes that we consider one possible way for simple and fast evaluation of primitives of products of a polynomial B-spl...

Efficient Evaluation of Triangular B-splines