B-SPLINE APPROXIMATION OF DISCONTINUOUS FUNCTIONS DEFINED ON A CLOSED CONTOUR IN THE COMPLEX PLANE - Capcelea, Maria; Capcelea, Titu (My University, 2022)
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.
Keywords: piecewise continuous function; closed contour; complex plane; approximation; B-spline; step function; convergence