Self-similarly corrected Padé approximants for the indeterminate problem
@article{Gluzman2015SelfsimilarlyCP, title={Self-similarly corrected Pad{\'e} approximants for the indeterminate problem}, author={Simon Gluzman and Vyacheslav I. Yukalov}, journal={The European Physical Journal Plus}, year={2015}, volume={131}, pages={1-21} }
Abstract.A method is suggested for treating the well-known deficiency in the use of Padé approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of self-similarly corrected Padé approximants, making it possible to essentially increase the class of functions treated by these approximants. The method works well even in those cases where the standard Padé approximants are not applicable, resulting…
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References
SHOWING 1-10 OF 90 REFERENCES
Convergence Rates of Padé and Padé-Type Approximants
- Mathematics
- 1996
A comparison is made between Pade and Pade-type approximants. LetQnbe thenth orthonormal polynomial with respect to a positive measure?with compact support inC. We show that for functions of the…
Self-similar factor approximants.
- Mathematics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003
It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions, and provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Padé approximant.
Padé approximants and efficient analytic continuation of a power series
- Mathematics
- 2002
This survey reflects the current state of the theory of Pade approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory,…
Extrapolation of perturbation-theory expansions by self-similar approximants
- MathematicsEuropean Journal of Applied Mathematics
- 2014
The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on…
EXTRAPOLATION OF POWER SERIES BY SELF-SIMILAR FACTOR AND ROOT APPROXIMANTS
- Physics
- 2004
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of…
Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators
- Mathematics
- 1998
The divergent Rayleigh-Schrodinger perturbation expansions for energy eigenvalues of cubic, quartic, sextic and octic oscillators are summed using algebraic approximants. These approximants are…
Method of self‐similar approximations
- Physics
- 1991
A new method is suggested to approximately find out the limit for a sequence of functions when solely several first terms of a sequence are known. The method seems to be very useful for those…
Pade and Hermite-Pade approximation and orthogonality
- Mathematics
- 2006
We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade approximation (simultaneous rational approximation to…