Viscovatov-Like Algorithm of Thiele–Newton’s Blending Expansion for a Bivariate Function

Li, Shengfeng; Dong, Yi

doi:10.3390/math7080696

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…However, this question will not be addressed in the present paper. Recurrent relations close to those discussed below and related to the extension of the Viskovatov algorithm to the case of Hermite-Padé polynomials were obtained in [19] and [14]; see also [6], [4], [18] and [5].…”

supporting

confidence: 73%

Viskovatov algorithm for Hermite-Padé polynomials

Ikonomov,

Suetin

2020

Preprint

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We propose an algorithm for producing Hermite-Padé polynomials of type I for an arbitrary tuple of m + 1 formal power series [f0, . . . , fm], m) under the assumption that the series have a certain ('general position') nondegeneracy property. This algorithm is a straightforward extension of the classical Viskovatov algorithm for construction of Padé polynomials (for m = 1 our algorithm coincides with the Viskovatov algorithm).The algorithm proposed here is based on a recurrence relation and has the feature that all the Hermite-Padé polynomials corresponding to the multiindices (k,

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supporting

confidence: 73%

Viskovatov algorithm for Hermite-Padé polynomials

Ikonomov,

Suetin

2020

Preprint

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“…The interpolation method plays a critical role in approximation theory and is a classical topic in numerical analysis [1][2][3][4][5][6]. It is believed that interpolation polynomial and rational interpolation are two popular interpolation methods.…”

Section: Introductionmentioning

confidence: 99%

“…Pahirya et al [4] developed the problem of the interpolant function of bivariate by two-dimensional continued fractions. Li et al [5] generalized Thiele's expansion of a univariate rational interpolation function to the Thiele-Newton blending rational interpolation. The authors also developed the Viscovatov-like algorithm to calculate the coefficients of Thiele-Newton's expansion.…”

Section: Introductionmentioning

confidence: 99%

Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points

et al. 2020

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The interpolation of Thiele-type continued fractions is thought of as the traditional rational interpolation and plays a significant role in numerical analysis and image interpolation. Different to the classical method, a novel type of bivariate Thiele-like rational interpolation continued fractions with parameters is proposed to efficiently address the interpolation problem. Firstly, the multiplicity of the points is adjusted strategically. Secondly, bivariate Thiele-like rational interpolation continued fractions with parameters is developed. We also discuss the interpolant algorithm, theorem, and dual interpolation of the proposed interpolation method. Many interpolation functions can be gained through adjusting the parameter, which is flexible and convenient. We also demonstrate that the novel interpolation function can deal with the interpolation problems that inverse differences do not exist or that there are unattainable points appearing in classical Thiele-type continued fractions interpolation. Through the selection of proper parameters, the value of the interpolation function can be changed at any point in the interpolant region under unaltered interpolant data. Numerical examples are given to show that the developed methods achieve state-of-the-art performance.

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A Viskovatov algorithm for Hermite-Padé polynomials

Ikonomov¹,

Suetin²

2021

Sb. Math.

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We propose and justify an algorithm for producing Hermite- Padé polynomials of type I for an arbitrary tuple of formal power series , , about the point ( ) under the assumption that the series have a certain (‘general position’) nondegeneracy property. This algorithm is a straightforward extension of the classical Viskovatov algorithm for constructing Padé polynomials (for our algorithm coincides with the Viskovatov algorithm). The algorithm is based on a recurrence relation and has the following feature: all the Hermite-Padé polynomials corresponding to the multi- indices , , , , are already known at the point when the algorithm produces the Hermite-Padé polynomials corresponding to the multi- index . We show how the Hermite-Padé polynomials corresponding to different multi-indices can be found recursively via this algorithm by changing the initial conditions appropriately. At every step , the algorithm can be parallelized in independent evaluations. Bibliography: 30 titles.

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Viscovatov-Like Algorithm of Thiele–Newton’s Blending Expansion for a Bivariate Function

Cited by 4 publications

References 18 publications

Viskovatov algorithm for Hermite-Padé polynomials

Viskovatov algorithm for Hermite-Padé polynomials

Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points

A Viskovatov algorithm for Hermite-Padé polynomials

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