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https://hdl.handle.net/20.500.14094/90007781
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2024-04-27
06:54 集計
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90007781 (fulltext)
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メタデータID
90007781
アクセス権
open access
出版タイプ
Accepted Manuscript
タイトル
Toward the best algorithm for approximate GCD of univariate polynomials
著者
著者ID
A1677
研究者ID
1000070359909
KUID
https://kuid-rm-web.ofc.kobe-u.ac.jp/search/detail?systemId=481c60126393dc1f520e17560c007669
著者名
Nagasaka, Kosaku
長坂, 耕作
ナガサカ, コウサク
所属機関名
人間発達環境学研究科
収録物名
Journal of Symbolic Computation
巻(号)
105
ページ
4-27
出版者
Elsevier
刊行日
2021-08
公開日
2023-09-01
抄録
Approximate polynomial GCD (greatest common divisor) of polynomials with a priori errors on their coefficients, is one of interesting problems in Symbolic-Numeric Computations. In fact, there are many known algorithms: QRGCD, UVGCD, STLN based methods, Fastgcd and so on. The fundamental question of this paper is “which is the best?” from the practical point of view, and subsequently “is there any better way?” by any small extension, any effect by pivoting, and any combination of sub-routines along the algorithms. In this paper, we consider a framework that covers those algorithms and their sub-routines, and makes their sub-routines being interchangeable between the algorithms (i.e. disassembling the algorithms and reassembling their parts). By this framework along with/without small new extensions and a newly adapted refinement sub-routine, we have done many performance tests and found the current answer. In summary, 1) UVGCD is the best way to get smaller tolerance, 2) modified Fastgcd is better for GCD that has one or more clusters of zeros with large multiplicity, and 3) modified ExQRGCD is better for GCD that has no cluster of zeros.
キーワード
Symbolic-numeric algorithm for polynomials
Approximate polynomial GCD
Subresultant matrix
Sylvester matrix
QR factorization
Rank structured matrix
カテゴリ
人間発達環境学研究科
学術雑誌論文
権利
© 2020 Elsevier Ltd.
This manuscript version is made available under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license.
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資源タイプ
journal article
言語
English (英語)
ISSN
0747-7171
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eISSN
1095-855X
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NCID
AA10460294
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関連情報
DOI
https://doi.org/10.1016/j.jsc.2019.08.004
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