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B-SPLINE APPROXIMATION OF DISCONTINUOUS FUNCTIONS DEFINED ON A CLOSED CONTOUR IN THE COMPLEX PLANE
(2022) Capcelea, Maria; Capcelea, Titu
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.
ALGORITHM FOR THE LOCALIZATION OF SINGULARITIES OF FUNCTIONS DEFINED ON CLOSED CONTOURS
(CEP USM, 2017) Capcelea, Maria; Capcelea, Titu
A numerical algorithm for locating polar singularities of functions defined on a discrete set of points of a simple closed contour in the complex plane is examined. The algorithm uses the Faber-Pad ́e approximation of the function and the fact that the zeros of its denominator give us approximations of the poles of function. The numerical performance of the algorithm is being analyzed on test issues.