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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Mari M(y) menjadi matriks yang entrinya adalah polinomial dalam y, λ(y) dan v(y) menjadi set nilai eigen dan vektor eigen bagi M(y). Kemudian, λ(y) dan v(y) ialah fungsi algebra bagi y, dan λ(y) dan v(y) mempunyai pengembangan siri kuasa mereka
λ(y) = β0 + β1 y +
v(y) = γ0 + γ1 y +
dengan syarat bahawa y=0 bukan titik tunggal λ(y) Atau v(y). Beberapa algoritma telah pun dicadangkan untuk mengira pengembangan siri kuasa di atas menggunakan kaedah Newton (algoritma dalam [4]) atau pembinaan Hensel (algoritma dalam [5],[12]). Algoritma yang dicadangkan setakat ini mengira pekali darjah tinggi βk dan γk, menggunakan pekali darjah rendah βj dan γj (j= 0,1,
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Salinan
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
Salinan
@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},}
Salinan
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 -