We consider here a two sided interpolation problem where we want to minimize the degree of the interpolant. We show that this degree is given by the rank of a particular solution to a Sylvester equation which, in some particular cases becomes a Löwner or a Hankel matrix. We consider an application to the usual partial realization problem. The results are quite general and no particular assumpti...

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...

Assuming only that the spectra of A and B are disjoint as opposed to the more restrictive assumption previously used, we obtain a bound in all unitarily invariant norms on the solution to the structured Sylvester equation AX − XB = A1/2EB1/2. This bound is the first of its kind in all unitarily invariant norms under only the disjointedness assumption. An application of the bound to the relative...

This paper presents a new version of the successive approximationsmethod for solving Sylvester equationsAX XB = C, where A and B are symmetric negative and positive definite matrices, respectively. This method is based on the block GMRES-Sylvester method. We also discuss the convergence of the new method. Some numerical experiments for obtaining the numerical solution of Sylvester equations are...

The Sylvester equation and its particular case, the Lyapunov equation, are widely used in image processing, control theory, stability analysis, signal model reduction, many more. We present basis-free solution to Clifford (geometric) algebra of arbitrary dimension. solutions involve only operations product, summation, conjugation. To obtain results, we use concepts characteristic polynomial, de...