Standard

Rational Interpolation: Jacobi’s Approach Reminiscence. / Утешев, Алексей Юрьевич; Боровой, Иван Иванович; Калинина, Елизавета Александровна.

In: Symmetry, Vol. 13, No. 8, 1401, 01.08.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Утешев, АЮ, Боровой, ИИ & Калинина, ЕА 2021, 'Rational Interpolation: Jacobi’s Approach Reminiscence', Symmetry, vol. 13, no. 8, 1401. https://doi.org/10.3390/sym13081401

APA

Утешев, А. Ю., Боровой, И. И., & Калинина, Е. А. (2021). Rational Interpolation: Jacobi’s Approach Reminiscence. Symmetry, 13(8), [1401]. https://doi.org/10.3390/sym13081401

Vancouver

Утешев АЮ, Боровой ИИ, Калинина ЕА. Rational Interpolation: Jacobi’s Approach Reminiscence. Symmetry. 2021 Aug 1;13(8). 1401. https://doi.org/10.3390/sym13081401

Author

Утешев, Алексей Юрьевич ; Боровой, Иван Иванович ; Калинина, Елизавета Александровна. / Rational Interpolation: Jacobi’s Approach Reminiscence. In: Symmetry. 2021 ; Vol. 13, No. 8.

BibTeX

@article{859e5eda31874ce29d4028b3c457f7d4,
title = "Rational Interpolation: Jacobi{\textquoteright}s Approach Reminiscence",
abstract = "We treat the interpolation problem { f (x j ) = y j } Nj=1 for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like {∑ Nj=1 xkj y j /W ′ (x j )} k ∈N and {∑ Nj=1 xkj /(y j W ′ (x j ))} k ∈N; here, W(x) = ∏ Nj=1 (x − x j ). We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials p(x) and q(x) given a set of values {p(x j )/q(x j )} Nj=1 is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point. ",
keywords = "Berlekamp–massey algorithm, Hankel matrices and polynomials, Polynomial interpolation, Rational interpolation, Resultant, resultant, Berlekamp-Massey algorithm, polynomial interpolation, rational interpolation",
author = "Утешев, {Алексей Юрьевич} and Боровой, {Иван Иванович} and Калинина, {Елизавета Александровна}",
year = "2021",
month = aug,
day = "1",
doi = "10.3390/sym13081401",
language = "English",
volume = "13",
journal = "Symmetry",
issn = "2073-8994",
publisher = "MDPI AG",
number = "8",

}

RIS

TY - JOUR

T1 - Rational Interpolation: Jacobi’s Approach Reminiscence

AU - Утешев, Алексей Юрьевич

AU - Боровой, Иван Иванович

AU - Калинина, Елизавета Александровна

PY - 2021/8/1

Y1 - 2021/8/1

N2 - We treat the interpolation problem { f (x j ) = y j } Nj=1 for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like {∑ Nj=1 xkj y j /W ′ (x j )} k ∈N and {∑ Nj=1 xkj /(y j W ′ (x j ))} k ∈N; here, W(x) = ∏ Nj=1 (x − x j ). We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials p(x) and q(x) given a set of values {p(x j )/q(x j )} Nj=1 is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point.

AB - We treat the interpolation problem { f (x j ) = y j } Nj=1 for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like {∑ Nj=1 xkj y j /W ′ (x j )} k ∈N and {∑ Nj=1 xkj /(y j W ′ (x j ))} k ∈N; here, W(x) = ∏ Nj=1 (x − x j ). We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials p(x) and q(x) given a set of values {p(x j )/q(x j )} Nj=1 is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point.

KW - Berlekamp–massey algorithm

KW - Hankel matrices and polynomials

KW - Polynomial interpolation

KW - Rational interpolation

KW - Resultant

KW - resultant

KW - Berlekamp-Massey algorithm

KW - polynomial interpolation

KW - rational interpolation

UR - http://www.scopus.com/inward/record.url?scp=85112603459&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f6d21dd9-f248-3163-bf9f-b54b5f62539f/

U2 - 10.3390/sym13081401

DO - 10.3390/sym13081401

M3 - Article

VL - 13

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 8

M1 - 1401

ER -

ID: 84400875