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
하자 M(y)는 항목이 다항식인 행렬입니다. y, λ(y) and v(y)는 다음의 고유값과 고유벡터의 집합입니다. M(y). 그런 다음, λ(y) and v(y)는 다음의 대수 함수입니다. y, 및 λ(y) and v(y) 멱급수 확장이 있습니다.
λ(y) = β0 + β1 y +
v(y) = γ0 + γ1 y +
제공 y=0은 λ(의 특이점이 아닙니다.y) 또는 v(y). Newton의 방법([4]의 알고리즘) 또는 Hensel 구성([5],[12]의 알고리즘)을 사용하여 위의 멱급수 확장을 계산하기 위한 여러 알고리즘이 이미 제안되었습니다. 지금까지 제안된 알고리즘은 높은 수준의 계수 β를 계산합니다.k 및 γk, 낮은 차수 계수 β 사용j 및 γj (j= 0,1,
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부
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
부
@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},}
부
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 -