Geodesic
Laurent-Pad\'e approximation for locating singularities of meromorphic functions with values given on simple closed contours
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 76-87.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper the Padé approximation with Laurent polynomials is examined for a meromorphic function on a finite domain of the complex plane. Values of the function are given at the points of a simple closed contour from this domain. Based on this approximation, an efficient numerical algorithm for locating singular points of the function is proposed. 
@article{BASM_2020_2_a7,
     author = {Maria Capcelea and Titu Capcelea},
     title = {Laurent-Pad\'e approximation for locating singularities of meromorphic functions with values given on simple closed contours},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {76--87},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2020_2_a7/}
}
TY  - JOUR
AU  - Maria Capcelea
AU  - Titu Capcelea
TI  - Laurent-Pad\'e approximation for locating singularities of meromorphic functions with values given on simple closed contours
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2020
SP  - 76
EP  - 87
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2020_2_a7/
LA  - en
ID  - BASM_2020_2_a7
ER  - 
%0 Journal Article
%A Maria Capcelea
%A Titu Capcelea
%T Laurent-Pad\'e approximation for locating singularities of meromorphic functions with values given on simple closed contours
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2020
%P 76-87
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2020_2_a7/
%G en
%F BASM_2020_2_a7
Maria Capcelea; Titu Capcelea. Laurent-Pad\'e approximation for locating singularities of meromorphic functions with values given on simple closed contours. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 76-87. http://geodesic.mathdoc.fr/item/BASM_2020_2_a7/

[1] Bultheel A., Laurent series and their Padé approximations, Birkhäuser Verlag, Basel–Boston, 1987 | MR

[2] Baker G., Graves-Morris P., Padé approximants, Second ed., Cambridge University Press, 1996 | MR

[3] Lyness J. N., “Differentiation formulas for analytic functions”, Math. Comp., 22:102 (1968), 352–362 | DOI | MR | Zbl

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