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Filters consist of a few resolvents to solve real symmetric definite generalized eigenproblems

  • Special Feature: Original Paper
  • International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2018)
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Abstract

By using a filter, we solve those eigenpairs of a real symmetric definite generalized eigenproblem \(A{\mathbf {v}}=\lambda B{\mathbf {v}}\) whose eigenvalues are in a specified real interval. In present study, the filter is a polynomial of the real-part of a linear combination of a few resolvents, and the polynomial is restricted to a Chebyshev polynomial to make the design of the filter simple. In order to apply a few resolvents, the same number of systems of linear equations with different shifts are solved. In present study, we assume those systems of linear equations are solved by some direct method using matrix factorizations. Since only a few resolvents are used, the number of required factorizations is also a few (2–4).

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  1. Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachi-Oji, Tokyo, 192-0397, Japan

    Hiroshi Murakami

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  1. Hiroshi Murakami
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Correspondence to Hiroshi Murakami.

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Murakami, H. Filters consist of a few resolvents to solve real symmetric definite generalized eigenproblems. Japan J. Indust. Appl. Math. 36, 579–618 (2019). https://doi.org/10.1007/s13160-019-00355-5

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  • DOI: https://doi.org/10.1007/s13160-019-00355-5

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