Saving flops in LU based shift-and-invert strategy |
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Authors: | Laura Grigori |
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Institution: | a INRIA Saclay-Ile de France, Laboratoire de Recherche en Informatique, Bât 490 Université Paris-Sud 11, 91405 Orsay Cedex, France b INRIA IRISA, Campus universitaire de Beaulieu, 35042 Rennes Cedex, France c School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China |
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Abstract: | The shift-and-invert method is very efficient in eigenvalue computations, in particular when interior eigenvalues are sought. This method involves solving linear systems of the form (A−σI)z=b. The shift σ is variable, hence when a direct method is used to solve the linear system, the LU factorization of (A−σI) needs to be computed for every shift change. We present two strategies that reduce the number of floating point operations performed in the LU factorization when the shift changes. Both methods perform first a preprocessing step that aims at eliminating parts of the matrix that are not affected by the diagonal change. This leads to about 43% and 50% flops savings respectively for the dense matrices. |
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Keywords: | 15A18 15A23 34L16 65F05 65F15 |
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