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
Deixei M(y) seja uma matriz cujas entradas são polinomiais em y,λ(y) e v(y) ser um conjunto de autovalor e autovetor de M(y). Então, λ(y) e v(y) são funções algébricas de ye λ(y) e v(y) têm suas expansões em série de potências
λ(y) = β0 + β1 y +
v(y) = γ0 +γ1 y +
providenciou que y=0 não é um ponto singular de λ(y) ou v(y). Vários algoritmos já são propostos para calcular as expansões de séries de potências acima usando o método de Newton (o algoritmo em [4]) ou a construção de Hensel (o algoritmo em [5],[12]). Os algoritmos propostos até agora calculam coeficientes de alto grau βk e γk, usando coeficientes de grau inferior βj e 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 -