Abstract
Two classes of structured Hermitian matrices are considered with the additional property that certain principal submatrices are all singular. Such matrices can be considered as the Pick matrices of certain (interior and boundary) norm constrained interpolation problems for functions meromorphic on the unit disk which the iterative Schur algorithm does not apply to. We characterize these matrices in terms of the parameters determining their structure and present formulas for their inertia.
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Bolotnikov, V. (2010). On Inertia of Some Structured Hermitian Matrices. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_7
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DOI: https://doi.org/10.1007/978-3-7643-8996-3_7
Publisher Name: Birkhäuser Basel
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