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Symbolic Computation of Eigenvalues, Eigenvectors and Generalized Eigenvectors of Matrices by Computer Algebra
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- Moritsugu Shuichi
- University of Library and Information Science
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- Kuriyama Kazuko
- National Institute of Informatics
Bibliographic Information
- Other Title
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- 行列の固有値・固有ベクトル・一般固有ベクトルの数式処理による記号的計算法
- ギョウレツ ノ コユウチ コユウ ベクトル イッパン コユウ ベクトル ノ スウシキ ショリ ニ ヨル キゴウテキ ケイサンホウ
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Description
We propose a symbolic formulation for computing eigenvalues, eigenvectors and generalized eigenvectors of rational matrices. Based on the Frobenius normal forms of matrices, our formulation constructs the eigenvectors without solving a system of linear equations by Gaussian elimination over an algebraic extension field. The experimental results show that our algorithm is more efficient than a conventional method implemented on the existing computer algebra systems. Although both Reduce and Maple failed for middle-sized matrices because of the memory problem, our program succeeded in solving the eigenproblem for much larger matrices.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 11 (2), 103-120, 2001
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390282680744543744
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- NII Article ID
- 110001878172
- 10011062837
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 5805215
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL Search
- CiNii Articles
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- Abstract License Flag
- Disallowed