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arXiv · 2001.02753

Locating conical degeneracies in the spectra of parametric self-adjoint matrices

Gregory Berkolaiko·Advait Parulekar
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Abstract

A simple iterative scheme is proposed for locating the parameter values for which a 2-parameter family of real symmetric matrices has a double eigenvalue. The convergence is proved to be quadratic. An extension of the scheme to complex Hermitian matrices (with 3 parameters) and to location of triple eigenvalues (5 parameters for real symmetric matrices) is also described. Algorithm convergence is illustrated in several examples: a real symmetric family, a complex Hermitian family, a family of matrices with an "avoided crossing" (no covergence) and a 5-parameter family of real symmetric matrices with a triple eigenvalue.

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BibTeXRIS

Gregory Berkolaiko, Advait Parulekar. 2020-01-08. Locating conical degeneracies in the spectra of parametric self-adjoint matrices. https://doi.org/10.1137/20m134174x

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