Geodesic
Electrostatics and ghost poles in near best fixed pole rational interpolation
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 439-452
We consider points that are near best for rational interpolation with prescribed poles in the same sense that Chebyshev points are near best for polynomial interpolation. It is shown that these interpolation points satisfy an electrostatic equilibrium problem involving the fixed poles and certain `ghost' poles. This problem is closely related to Lam$\acute e$ equations with residues of mixed sign.
Classification : 33C45, 42C05
Keywords: rational interpolation, Chebyshev weight, zeros, potential theory 
@article{ETNA_2007__26__a2,
     author = {Van Deun,  Joris},
     title = {Electrostatics and ghost poles in near best fixed pole rational interpolation},
     journal = {Electronic transactions on numerical analysis},
     pages = {439--452},
     year = {2007},
     volume = {26},
     zbl = {1176.33015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a2/}
}
TY  - JOUR
AU  - Van Deun,  Joris
TI  - Electrostatics and ghost poles in near best fixed pole rational interpolation
JO  - Electronic transactions on numerical analysis
PY  - 2007
SP  - 439
EP  - 452
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a2/
LA  - en
ID  - ETNA_2007__26__a2
ER  - 
%0 Journal Article
%A Van Deun,  Joris
%T Electrostatics and ghost poles in near best fixed pole rational interpolation
%J Electronic transactions on numerical analysis
%D 2007
%P 439-452
%V 26
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a2/
%G en
%F ETNA_2007__26__a2
Van Deun,  Joris. Electrostatics and ghost poles in near best fixed pole rational interpolation. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 439-452. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a2/