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Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
SIAM Journal on Scientific and Statistical Computing, 1986The method of \textit{E. R. Davidson} [J. Comput. Phys. 17, 87-94 (1975; Zbl 0293.65022)] for computing a few eigenpairs of large sparse symmetric matrices is analyzed as a method for using diagonal preconditioning (i.e. using an approximate inverse).
Morgan, Ronald B., Scott, David S.
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A hybrid method for the solution of sparse power system matrices on vector computers
38th Midwest Symposium on Circuits and Systems. Proceedings, 2002This paper describes a methodology for solving a linear system of equations on vector computer. The methodology combines direct and inverse factors. The decomposition and implementation of the direct solution in a CRAY Y-MPZE/232, and the performance results are discussed.
A. Padilha, A.R. Basso
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Summary: Obtaining high accuracy singular triplets for large sparse matrices is a significant challenge, especially when searching for the smallest triplets. Due to the difficulty and size of these problems, efficient methods must function iteratively, with preconditioners, and under strict memory constraints. In this research, we present a Golub-Kahan
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Computational methods for sparse matrices
Computer Physics Communications, 1980Abstract This paper is a survey of methods currently available for processing sparse matrices in a digital computer; specifically in the solution of linear algebraic equations and the eigenproblem.
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A New Method for Computing $��$-functions and Their Condition Numbers of Large Sparse Matrices
2016We propose a new method for computing the $ $-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of $ _{\ell}$-functions of a large matrix to $ _{\ell+1}$-functions of some $r$-by-$r$ matrices, where $r$ is the numerical rank of the large matrix in question.
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