Doubling algorithms and their applications

We present two structure-preserving doubling algorithms and apply them to solve several nonlinear matrix equations arising in control theory, quadratic eigenvalue problems, nano research, and Markov chains.

Some advanced results from operator theory are used to show the existence of special solutions of practical interest. The algorithms are shown to be well-defined for the applications. The convergence of these algorithms to the desired solutions is established for the nonsingular case as well as the singular case. A few open questions are also raised in the talk.