B-SPLINE APPROXIMATION OF DISCONTINUOUS FUNCTIONS DEFINED ON A CLOSED CONTOUR IN THE COMPLEX PLANE

Abstract

In this paper we propose an efficient algorithm for approximating piecewise continuous functions, defined on a closed contour Γ in the complex plane. The function, defined numerically on a finite set of points of Γ, is approximated by a linear combination of B-spline functions and Heaviside step functions, defined on Γ. Theoretical and practical aspects of the convergence of the algorithm are presented, including the vicinity of the discontinuity points.