Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building a new DRP scheme in the same time. keywords DRP schemes, Sylvester equation

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...

We derive the solvability conditions and a formula of general solution to Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate necessary sufficient for quaternion equation, which involves ?-Hermicity. also provide algorithm with numerical example illustrate main results this paper.

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...

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...

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...

The solution of large scale Sylvester matrix equation plays an important role in control and large scientific computations. A popular approach is to use the global GMRES algorithm. In this work, we first consider the global GMRES algorithm with weighting strategy, and propose some new schemes based on residual to update the weighting matrix. Due to the growth of memory requirements and computat...

In this paper, by extending the well-known Jacobi and Gauss–Seidel iterations for Ax = b, we study iterative solutions of matrix equations AXB = F and generalized Sylvester matrix equations AXB + CXD = F (including the Sylvester equation AX + XB = F as a special case), and present a gradient based and a least-squares based iterative algorithms for the solution. It is proved that the iterative s...