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Keywords
(7)
Analytic Function
Approximate Solution
Asymptotic Properties
Continued Fraction
Inverse Problem
Rational Approximation
Rational Interpolation
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Rational approximation of analytic functions
Rational approximation of analytic functions,10.1134/S0081543811030047,Proceedings of The Steklov Institute of Mathematics,A. A. Gonchar
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Rational approximation of analytic functions
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Citations: 4
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A. A. Gonchar
The paper provides an overview of the author’s contribution to the theory of constructive rational approximations of analytic functions. The results presented are related to the convergence theory of Padé approximants and of more general
rational interpolation
processes, which significantly expand the classical theory’s framework of continuous fractions, to inverse problems in the theory of Padé approximants, to the application of multipoint Padé approximants (solutions of CauchyJacobi interpolation problem) in explorations connected with the rate of Chebyshev
rational approximation
of analytic functions and to the
asymptotic properties
of PadéHermite approximation for systems of Markov type functions.
Journal:
Proceedings of The Steklov Institute of Mathematics  PROC STEKLOV INST MATH
, vol. 272, pp. 4457, 2011
DOI:
10.1134/S0081543811030047
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Citation Context
(1)
...3.3. Beforestatingthemaintheorem (see[
18
,19]), we introducethenecessary notation...
A. A. Gonchar
.
Rational approximation of analytic functions
References
(10)
a Local Condition for the SingleValuedness of Analytic Functions of Several Variables
(
Citations: 13
)
A. A. Goncar
Journal:
Mathematics of The Ussrsbornik
, vol. 22, no. 2, pp. 305322, 1974
The Rate of Rational Approximation and the Property of SingleValuedness of AN Analytic Function in the Neighborhood of AN Isolated Singular Point
(
Citations: 3
)
A. A. Goncar
Journal:
Mathematics of The Ussrsbornik
, vol. 23, no. 2, pp. 254270, 1974
On Convergence of PADÉ Approximants for Some Classes of Meromorphic Functions
(
Citations: 43
)
A. A. Goncar
Journal:
Mathematics of The Ussrsbornik
, vol. 26, no. 4, pp. 555575, 1975
On the Convergence of Generalized PADÉ Approximants of Meromorphic Functions
(
Citations: 31
)
A. A. Goncar
Journal:
Mathematics of The Ussrsbornik
, vol. 27, no. 4, pp. 503514, 1975
On the rate of rational approximation of analytic functions
(
Citations: 5
)
A. Gončar
,
E. A. Rakhmanov
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Citations
(4)
Rational approximation of analytic functions
(
Citations: 4
)
A. A. Gonchar
Journal:
Proceedings of The Steklov Institute of Mathematics  PROC STEKLOV INST MATH
, vol. 272, pp. 4457, 2011
Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle
(
Citations: 12
)
L. Baratchart
,
H. Stahl
,
F. Wielonsky
Journal:
Constructive Approximation  CONSTR APPROX
, vol. 17, no. 1, pp. 103138, 2001
Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions
(
Citations: 4
)
V. A. Prokhorov
,
E. B. Saff
Journal:
Constructive Approximation  CONSTR APPROX
, vol. 15, no. 2, pp. 155173, 1999
On the convergence of generalized Padé approximants
(
Citations: 21
)
Herbert Stahl
Journal:
Constructive Approximation  CONSTR APPROX
, vol. 5, no. 1, pp. 221240, 1989