Now showing items 1-16 of 16

• #### A note on the fixed-point iteration for the matrix equations $X\pm A^*X^{-1}A=I$ ﻿

(Elsevier, 2008)
The fixed-point iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations $X\pm A^*X^{-1}A=I$ (the plus/minus equations). The convergence of this method ...
• #### Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case ﻿

(SIAM, 2009)
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 ﻿

(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)