Geodesic
Approximation by Simplest Fractions
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 553-559

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In this paper, a number of problems concerning the uniform approximation of complex-valued continuous functions $f(z)$ on compact subsets of the complex plane by simplest fractions of the form $\Theta _n(z)=\sum _{j=1}^n1/(z-z_j)$ are considered. In particular, it is shown that the best approximation of a function $f$ by the fractions $\Theta _n$ is of the same order of vanishing as the best approximations by polynomials of degree $\le n$. 
@article{MZM_2001_70_4_a6,
     author = {V. I. Danchenko and D. Ya. Danchenko},
     title = {Approximation by {Simplest} {Fractions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {553--559},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a6/}
}
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V. I. Danchenko; D. Ya. Danchenko. Approximation by Simplest Fractions. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 553-559. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a6/