This Thesis contains contributions in two different but closely related subfields of Scientific and Parallel Computing which arise in the context of various eigenvalue problems: periodic and parallel eigenvalue reordering and parallel algorithms for Sylvestertype matrix equations with applications in condition estimation. Many real world phenomena behave periodically, e.g., helicopter rotors, r...

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 relatively new branch of computational biology and chemistry has been emerging as an e ort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the structure of molecules, embedding them in Euclidean space, and nding the energetically favorable con gurations. We illustrate several e cient algebraic algorithms for enumerating all possible conformations ...

The inverse condictivity problem with many boundary measurements consists of recovery of conductivity coefficient a (principal part) of an elliptic equation in a domain Ω ⊂ R, n = 2, 3 from the Neumann data given for all Dirichlet data (Dirichlet-to-Neumann map). Calderon [5] proposed the idea of using complex exponential solutions to demonstrate uniqueness in the linearized inverse condictivit...

Abstract—A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitraril...

This paper aims at finding a fixed-time solution to the Sylvester equation by using gradient neural network (GNN). To reach this goal, modified sign-bi-power (msbp) function is presented and applied on linear GNN as an activation function. Accordingly, convergent (FTC-GNN) model developed for solving equation. The upper bound of convergence time such FTC-GNN can be predetermined if parameters a...

This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems ...

We consider the numerical approximation to the solution of the matrix equation A1X+XA2 −Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A1, A2 of large dimensions. We propose a new formulation of the problem that entails the numerical solution of an unconstrained Sylvester equation. The spectral properties of the resulting coefficient matrices call for appropriately des...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...