Geodesic
B-spline approximation of discontinuous functions defined on a closed contour in the complex plane
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2022), pp. 59-67 
Maria Capcelea; Titu Capcelea. B-spline approximation of discontinuous functions defined on a closed contour in the complex plane. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2022), pp. 59-67. http://geodesic.mathdoc.fr/item/BASM_2022_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] J. H. Ahlberg, E. N. Nilson, J. L. Walsh, “Complex cubic splines”, Tran. Am. Math. Soc., 129 (1967), 391–413 | DOI | MR

[2] G. Walz, “B-Splines im Komplexen”, Complex Variables, Theory Appl., 15:2 (1990), 95–105 | DOI | MR

[3] M. Capcelea, T. Capcelea, “Algorithms for efficient and accurate approximation of piecewise continuous functions”, Abstracts of the International Scientific Conference “Mathematics Information Technologies: Research and Education (MITRE-)” dedicated to the 70th anniversary (Moldova State University, Chisinau, June 23-26, 2016), 2016, 15

[4] M. Capcelea, T. Capcelea, “Localization of singular points of meromorphic functions based on interpolation by rational functions”, Bul. Acad. Ştiinţe Repub. Mold., Mat., 2021, no. 1–2(95–96), 110–120 | MR

[5] M. Capcelea, T. Capcelea, “Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours”, Bul. Acad. Ştiinţe Repub. Mold., Mat., 2020, no. 2(93), 76–87 | MR