Abstract
We consider the generalized eigenvalue problem A x = λB x, where A and B are real symmetric matrices and B is also positive definite. All the eigenvalues of this problem are real, and it is often necessary to compute only a few eigenvalues which are important for applications. In electronic structure calculations of materials, specific interior eigenvalues are of fundamental interest, since they play crucial roles in various industrial applications. In this paper, we propose an approach based on the inertia of the linear matrix pencil of A and B. The eigenvalue problem is restated, and a class of algorithms is presented for separating the target eigenvalues from the others.
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This work was partially supported by KAKENHI Grant Numbers 24760061, 21760058, and 22104004.
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Lee, D., Miyata, T., Sogabe, T. et al. An interior eigenvalue problem from electronic structure calculations. Japan J. Indust. Appl. Math. 30, 625–633 (2013). https://doi.org/10.1007/s13160-013-0118-0
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DOI: https://doi.org/10.1007/s13160-013-0118-0