A Practical Implementation of Modular Algorithms for Frobenius Normal Forms of Rational Matrices
書誌事項
- タイトル別名
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- Practical Implementation of Modular Algorithms for Frobenius Normal Forms of Rational Matrices
- アルゴリズム理論
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説明
Modular algorithms for computing the Frobenius normal forms of integer and rational matrices are presented and their implementation is reported. These methods compute Frobenius normal forms over Zpi where pi's are distinct primes and then construct the normal forms over Z or Q by the Chinese remainder theorem. Our implementation includes: (1) detection of unlucky primes (2) a new formula for the efficient computation of a transformation matrix and (3) extension of our preceding algorithm over Z to one over Q. Through experiments using a number of test matrices we confirm that our modular algorithm is more efficient in practical terms than the straightforward implementation of conventional methods.
Modular algorithms for computing the Frobenius normal forms of integer and rational matrices are presented and their implementation is reported. These methods compute Frobenius normal forms over Zpi, where pi's are distinct primes, and then construct the normal forms over Z or Q by the Chinese remainder theorem. Our implementation includes: (1) detection of unlucky primes, (2) a new formula for the efficient computation of a transformation matrix, and (3) extension of our preceding algorithm over Z to one over Q. Through experiments using a number of test matrices, we confirm that our modular algorithm is more efficient in practical terms than the straightforward implementation of conventional methods.
収録刊行物
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- 情報処理学会論文誌
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情報処理学会論文誌 45 (6), 1630-1641, 2004-06-15
一般社団法人情報処理学会
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詳細情報 詳細情報について
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- CRID
- 1050001337883745920
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- NII論文ID
- 110002712211
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- NII書誌ID
- AN00116647
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- ISSN
- 18827764
- 03875806
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- HANDLE
- 2241/00134699
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- NDL書誌ID
- 6990111
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- 本文言語コード
- en
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- journal article
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