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• Detecting and solving hyperbolic quadratic eigenvalue problems ﻿

(SIAM, 2009)
Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with ...
• An Improved Arc Algorithm for Detecting Definite Hermitian Pairs ﻿

(SIAM, 2009)
A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair $(A,B)$ is definite by exploring the range of the function \$f(x) = x^*(A + iB)x/|x^*(A + ...