Geodesic
Localization of singular points of meromorphic functions based on interpolation by rational functions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 110-120.

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In this paper we examine two algorithms for localization of singular points of meromorphic functions. Both algorithms apply approximation by interpolation with rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain that includes a simple closed contour on which the values of the function are known. The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour where the function values are given. 
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Maria Capcelea; Titu Capcelea. Localization of singular points of meromorphic functions based on interpolation by rational functions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2021), pp. 110-120. https://geodesic-test.mathdoc.fr/item/BASM_2021_1_a6/

[1] H. Kang, H. Lee, “Identification of Simple Poles via Boundary Measurements and an Application of EIT”, Inverse Problems, 20 (2004), 1853–1863 | DOI | MR | Zbl

[2] Miller K., “Stabilized numerical analytic prolongation with poles”, SIAM J. Appl. Math., 18 (1970), 346–363 | DOI | MR | Zbl

[3] Nara T., Ando S., “Direct localization of poles of a meromorphic function from measurements on an incomplete boundary”, Inverse Problems, 26 (2010), 1–26 | DOI | MR | Zbl

[4] Capcelea M., Capcelea T., “Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours”, Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2020, no. 2(93), 76–87 | MR | Zbl

[5] Capcelea M., Capcelea T., “Algorithm for the localization of singularities of functions defined on closed contours”, Proceedings of the 4th Conference of Mathematical Society of Moldova, CMSM4-2017 (June 28-July 2, 2017, Chisinau, Republic of Moldova), 369–372

[6] Gonnet P., Pachon R., Trefethen L., “Robust rational interpolation and least-squares”, Electronic Transactions on Numerical Analysis, 38 (2011), 146–167 | MR | Zbl

[7] Saff E., “An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions”, Journal of Approximation Theory, 6 (1972), 63–67 | DOI | MR | Zbl

[8] Saff E., Walsh J., “On the convergence of rational functions which interpolate in the roots of unity”, Pacific Journal of Mathematics, 45 (1973), 639–641 | DOI | MR | Zbl

[9] Yan C.-D., Chieng W.-H., “Method for finding multiple roots of polynomials”, Computers and Mathematics with Applications, 51 (2006), 605–620 | DOI | MR | Zbl

[10] Gonnet P., Guttel S., Trefethen L. N., “Robust Padé approximation via SVD”, SIAM Review, 55:1 (2013), 101–117 | DOI | MR | Zbl