Geodesic
Pad\'e--Faber Approximation of Markov Functions on Real-Symmetric Compact Sets
Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 81-94

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Study of Padé–Faber approximation (generalizations of the Padé approximation and the Padé–Chebyshev approximation) of Markov functions are important not only from the point of view of mathematical analysis, but also of computational mathematics. The theorem on the existence of subdiagonal approximants is constructively proved. Various estimates of the approximation error are given. Theoretical assertions are illustrated by simulation results.
Keywords: Padé–Faber approximation, Markov function, Padé–Chebyshev approximation, subdiagonal approximant, Lanczos process, Faber operator, extended complex plane. 
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     author = {L. A. Knizhnerman},
     title = {Pad\'e--Faber {Approximation} of {Markov} {Functions} on {Real-Symmetric} {Compact} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {81--94},
     publisher = {mathdoc},
     volume = {86},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a6/}
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L. A. Knizhnerman. Pad\'e--Faber Approximation of Markov Functions on Real-Symmetric Compact Sets. Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 81-94. http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a6/