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Locating Conical Degeneracies in the Spectra of Parametric Self-adjoint Matrices
A simple iterative scheme is proposed for locating the parameter values for which a two-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 three parameters) and to the location of triple eigenvalues (five 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 convergence), and a five-parameter family of real symmetric matrices with a triple eigenvalue.
Read More: https://epubs.siam.org/doi/abs/10.1137/20M134174X
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