LOW-RANK SOLUTION METHODS FOR LARGE-SCALE LINEAR MATRIX EQUATIONS Stephen D. Shank DOCTOR OF PHILOSOPHY Temple University, May, 2014 Professor Daniel B. Szyld, Chair We consider low-rank solution methods for certain classes of large-scale linear matrix equations. Our aim is to adapt existing low-rank solution methods based on standard, extended and rational Krylov subspaces to solve equations w...

A class of new observers in descriptor linear systems, proportional-derivative (PD) observers, are proposed. A parametric design approach for such observers is proposed based on a complete parametric solution to the generalized Sylvester matrix equation. The approach provides complete parameterizations for all the observer gains, gives the parametric expression for the corresponding left eigenv...

We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The is always applicable any given initial and will arrive at LS solution within finite steps. When the equation has many solutions, can search one with minimal Frobenius-norm. Moreover, Y, find unique closest Y. Numerical experim...

In this short note we deal with a constructive scheme to decompose a continuous family of matrices A(ρ) asymptotically as ρ → 0 into blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also discuss the extension of the scheme to matrix families depending upon additional parameters and operators on Hilbert spaces. 1. Matrix theory 1.1. Preliminaries. We first recall some w...

Imagine the following scenario. You are in your overpriced hotel room, reviewing your notes for an important presentation that you will be giving later in the day. The people next door have their television cranked to maximum volume. It is so loud that you can hear the dialogue as well as the gunfire and explosions; it is from Sylvester Stallone's movie Judge Dredd. Despite an earlier request t...

Abstract A method for computing an approximate inverse preconditioner of a matrix A which all eigenvalues have negative real parts is proposed. The approximate solution of the special Sylvester matrix equation AX+ XA = I, which is an approximate inverse preconditioner of matrix A, is obtaining by the successive approximations method. Some numerical experiments on test matrices from Harwell-Boin...