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arXiv · 2208.01359

Solving singular generalized eigenvalue problems. Part II: projection and augmentation

Michiel E. Hochstenbach·Christian Mehl·Bor Plestenjak
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Abstract

Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two alternative methods. The first technique is based on a projection onto subspaces with dimension equal to the normal rank of the pencil while the second approach exploits an augmented matrix pencil. The projection approach seems to be the most attractive version for generic singular pencils because of its efficiency, while the augmented pencil approach may be suitable for applications where a linear system with the augmented pencil can be solved efficiently.

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Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak. 2022-08-02. Solving singular generalized eigenvalue problems. Part II: projection and augmentation. https://doi.org/10.1137/22m1513174

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