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CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems. (English) Zbl 1156.65035
Given large real symmetric matrices $$A$$ and $$B$$, with $$B$$ positive definite, the authors consider a method for computing those eigenvalues of $$Ax=\lambda Bx$$ which lie in a given region, and also computing the corresponding eigenvectors. The method uses a contour integral to construct a subspace for Rayleigh–Ritz projection. Evaluation of the integral requires the solution of a number of systems of linear equations, which may be solved in parallel. The method is compared numerically with an earlier method of the first author and H. Sugiura [J. Comput. Appl. Math. 159, No. 1, 119–128 (2003; Zbl 1037.65040)].

##### MSC:
 65F15 Numerical computation of eigenvalues and eigenvectors of matrices
CIRR
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