Journal ArticleDOI
Solving the eigenvalue problem for sparse matrices
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TLDR
A modification of the Danilewski method is presented, permitting the solution of the eigenvalue problem for a constant sparse matrix of large order to be reduced to the solution for a polynomial matrix of lower order.Abstract:
A modification of the Danilewski method is presented, permitting the solution of the eigenvalue problem for a constant sparse matrix of large order to be reduced to the solution of the same problem for a polynomial matrix of lower order. Certain solution algorithms are proposed for a partial eigenvalue problem for the polynomial matrix. Questions of the realization of the algorithms on a model PRORAB computer are examined.read more
Citations
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Journal ArticleDOI
Realization of matrix operations for the PRORAB computer
TL;DR: The article is devoted to the computer realization of well-known computational algorithms of linear algebra with sparse matrices, as well as sub-schemes realizing the normalized expansion of a matrix and the modified Danilewski method.
Journal ArticleDOI
Effective construction of eigenvectors for a class of singular sparse matrices
Xiaoying Han,Habib N. Najm +1 more
TL;DR: Fundamental results and an efficient algorithm for constructing eigenvectors corresponding to non-zero eigenvalues of matrices with zero rows and/or columns are developed.
Journal ArticleDOI
A model prorab machine and solution of problems with very sparse quantities
TL;DR: The paper presents the latest version of programs implementing the large-block operating mode in machines of the M-20 family with orientation to the solution of problems with very sparse quantities.
References
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Journal ArticleDOI
Computational Methods of Linear Algebra
Journal ArticleDOI
Computational methods of linear algebra
D. K. Faddeev,V. N. Faddeeva +1 more
TL;DR: A survey of computational methods in linear algebra can be found in this article, where the authors discuss the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, and more traditional questions such as algebraic eigenvalue problems and systems with a square matrix.
Journal ArticleDOI
On a certain approach to the problem orientation of electronic computers
T. N. Smiraova,N. B. Malyshev +1 more
Journal ArticleDOI
Realization of matrix operations for the PRORAB computer
TL;DR: The article is devoted to the computer realization of well-known computational algorithms of linear algebra with sparse matrices, as well as sub-schemes realizing the normalized expansion of a matrix and the modified Danilewski method.