Now showing items 1-3 of 3
Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case
In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical ...
Detecting and solving hyperbolic quadratic eigenvalue problems
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
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 + ...