B-spline approximation of discontinuous functions defined on a closed contour in the complex plane

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