The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Laisser nous M(y) être une matrice dont les entrées sont polynomiales dans y, λ(y) et v(y) être un ensemble de valeurs propres et de vecteurs propres de M(y). Alors, λ(y) et v(y) sont des fonctions algébriques de y, et λ(y) et v(y) ont leurs extensions en séries entières
λ(y) = β0 + β1 y +
v(y) = y0 + y1 y +
à condition que y=0 n’est pas un point singulier de λ(y) ou v(y). Plusieurs algorithmes sont déjà proposés pour calculer les développements en séries entières ci-dessus en utilisant la méthode de Newton (l'algorithme de [4]) ou la construction de Hensel (l'algorithme de [5], [12]). Les algorithmes proposés jusqu'à présent calculent des coefficients β de haut degrék et γk, en utilisant des coefficients de degré inférieur βj et γj (j= 0,1,
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Takuya KITAMOTO, Tetsu YAMAGUCHI, "On the Check of Accuracy of the Coefficients of Formal Power Series" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 8, pp. 2101-2110, August 2008, doi: 10.1093/ietfec/e91-a.8.2101.
Abstract: Let M(y) be a matrix whose entries are polynomial in y, λ(y) and v(y) be a set of eigenvalue and eigenvector of M(y). Then, λ(y) and v(y) are algebraic functions of y, and λ(y) and v(y) have their power series expansions
λ(y) = β0 + β1 y +
v(y) = γ0 + γ1 y +
provided that y=0 is not a singular point of λ(y) or v(y). Several algorithms are already proposed to compute the above power series expansions using Newton's method (the algorithm in [4]) or the Hensel construction (the algorithm in[5],[12]). The algorithms proposed so far compute high degree coefficients βk and γk, using lower degree coefficients βj and γj (j=0,1,
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.8.2101/_p
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@ARTICLE{e91-a_8_2101,
author={Takuya KITAMOTO, Tetsu YAMAGUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Check of Accuracy of the Coefficients of Formal Power Series},
year={2008},
volume={E91-A},
number={8},
pages={2101-2110},
abstract={Let M(y) be a matrix whose entries are polynomial in y, λ(y) and v(y) be a set of eigenvalue and eigenvector of M(y). Then, λ(y) and v(y) are algebraic functions of y, and λ(y) and v(y) have their power series expansions
λ(y) = β0 + β1 y +
v(y) = γ0 + γ1 y +
provided that y=0 is not a singular point of λ(y) or v(y). Several algorithms are already proposed to compute the above power series expansions using Newton's method (the algorithm in [4]) or the Hensel construction (the algorithm in[5],[12]). The algorithms proposed so far compute high degree coefficients βk and γk, using lower degree coefficients βj and γj (j=0,1,
keywords={},
doi={10.1093/ietfec/e91-a.8.2101},
ISSN={1745-1337},
month={August},}
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TY - JOUR
TI - On the Check of Accuracy of the Coefficients of Formal Power Series
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2101
EP - 2110
AU - Takuya KITAMOTO
AU - Tetsu YAMAGUCHI
PY - 2008
DO - 10.1093/ietfec/e91-a.8.2101
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2008
AB - Let M(y) be a matrix whose entries are polynomial in y, λ(y) and v(y) be a set of eigenvalue and eigenvector of M(y). Then, λ(y) and v(y) are algebraic functions of y, and λ(y) and v(y) have their power series expansions
λ(y) = β0 + β1 y +
v(y) = γ0 + γ1 y +
provided that y=0 is not a singular point of λ(y) or v(y). Several algorithms are already proposed to compute the above power series expansions using Newton's method (the algorithm in [4]) or the Hensel construction (the algorithm in[5],[12]). The algorithms proposed so far compute high degree coefficients βk and γk, using lower degree coefficients βj and γj (j=0,1,
ER -