Geodesic
Pad\'e approximants and efficient analytic continuation of a~power series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 1, pp. 43-141

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

This survey reflects the current state of the theory of Padé approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence of Padé approximants of this series. Row and diagonal sequences are studied from this point of view. Gonchar's and Rakhmanov's fundamental results of inverse nature are presented along with results of the author. 
@article{RM_2002_57_1_a1,
     author = {S. P. Suetin},
     title = {Pad\'e approximants and efficient analytic continuation of a~power series},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {43--141},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2002_57_1_a1/}
}
TY  - JOUR
AU  - S. P. Suetin
TI  - Pad\'e approximants and efficient analytic continuation of a~power series
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 43
EP  - 141
VL  - 57
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2002_57_1_a1/
LA  - en
ID  - RM_2002_57_1_a1
ER  - 
%0 Journal Article
%A S. P. Suetin
%T Pad\'e approximants and efficient analytic continuation of a~power series
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 43-141
%V 57
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2002_57_1_a1/
%G en
%F RM_2002_57_1_a1
S. P. Suetin. Pad\'e approximants and efficient analytic continuation of a~power series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 1, pp. 43-141. http://geodesic.mathdoc.fr/item/RM_2002_57_1_a1/