Padé Approximants in Complex Points Revisited

Hebhoub, Fahima; Yushchenko, Lidiya

doi:10.1155/2011/324865

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…If we compare this method with the traditional Pade´approximant, we can observe that this method usually gives more accurate results and enjoys the same low cost as the traditional Pade´approximant. We will now recall some definitions and results related to the N-point Pade´approximants [39].…”

Section: N-point Padé Approximantsmentioning

confidence: 99%

A comprehensive study of the mathematical methods used to approximate the inverse Langevin function

Jedynak

2018

Mathematics and Mechanics of Solids

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This paper is motivated by Marchi and Arruda (Math Mech Solids, 2018), who developed numerous approximations to the inverse Langevin function, minimizing their maximum relative error with the help of special software. We are convinced that this method, together with the minimax approximation, is the most robust and versatile approximation algorithm. It uses one of the first objective functions developed by differential evolution. It guarantees the best solution in one trial. In previous papers, a constraint on the error function of the inverse Langevin function was imposed, but here we discuss the approximants resulting from various types of constraint. The evolution of the different mathematical methods that have been used to approximate the inverse Langevin function will also be treated, providing a useful starting point for researchers beginning to work in the field of approximation theory. To categorize the existing solutions, we find the optimal approximations of the inverse Langevin function for a given complexity and for different constraints on the error function.

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Section: N-point Padé Approximantsmentioning

confidence: 99%

A comprehensive study of the mathematical methods used to approximate the inverse Langevin function

Jedynak

2018

Mathematics and Mechanics of Solids

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Generalized Moment Representations and Multivariate Multipoint Padé Approximants

2020

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Distributions of zeros and poles of -point Padé approximants to complex-symmetric functions defined at complex points

Jedynak

Gilewicz

2021

Ukr. Mat. Zhurn.

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UDC 517.5 The knowledge of the location of zeros and poles Padé and -point Padé approximations to a given function provides much valuable information about the function being studied.In general PAs reproduce the exact zeros and poles of considered function, but, unfortunately, some spurious zeros and poles appear randomly.Then, it is clear that the control of the position of poles and zeros becomes essential for applications of Padé approximation method.The numerical examples included in the paper show how necessary for the convergence of PA is the knowledge of the position of their zeros and poles.We relate our research of localization of poles and zeros of PA and NPA in the case of Stieltjes functions because we are interested in the efficiency of numerical application of these approximations. These functions belong to the class of complex-symmetric functions.The PA and NPA to the Stieltjes functions in different regions of the complex plane is also analyzed. It is expected that the appropriate selection of the complex point for the definition of approximant can improve it with respect to the traditional choice of All considered cases are graphically illustrated.Some unique numerical results presented in the paper, which are sufficiently regular should motivate the reader to reflect on them.

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Padé Approximants in Complex Points Revisited

Cited by 3 publications

References 3 publications

A comprehensive study of the mathematical methods used to approximate the inverse Langevin function

A comprehensive study of the mathematical methods used to approximate the inverse Langevin function

Generalized Moment Representations and Multivariate Multipoint Padé Approximants

Distributions of zeros and poles of -point Padé approximants to complex-symmetric functions defined at complex points

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