LOCATING CONICAL DEGENERACIES IN THE SPECTRA OF PARAMETRIC SELF-ADJOINT MATRICES

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.

authors

• Berkolaiko, Gregory

published proceedings

• SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

altmetric score

• 0.75

author list (cited authors)

• Berkolaiko, G., & Parulekar, A.

citation count

• 1

complete list of authors

• Berkolaiko, Gregory||Parulekar, Advait

publication date

• January 2021

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Matrix Analysis and Applications  Journal

keywords

• Conical Points
• Dirac Points
• Dispersion Relation
• Eigenvalue Multiplicity
• Parametric Families Of Self-adjoint Matrices

Digital Object Identifier (DOI)

• 10.1137/20M134174X

start page

• 224

end page

• 242

volume

• 42

issue

• 1

URL

• http://dx.doi.org/10.1137/20m134174x