SYMMETRICAL MATRIX POLYNOMIAL EQUATION - INTERPOLATION RESULTS

New numerical procedures are proposed to solve the symmetric matrix po lynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequent ly encountered in control and signal processing. An interpolation appr oach is presented that takes full advantage of symmetry properties and leads to an equivalent reduced-size linear system of equations. It re sults in a simple and general characterization of all solutions of exp ected column degrees. Several new theoretical results concerning stabi lity theory and reduced Sylvester resultant matrices are also develope d and used to conclude a priori on the existence of a solution. By mea ns of numerical experiments, it is shown that our algorithms are more efficient than older methods and, namely, appear to be numerically rel iable. (C) 1998 Elsevier Science Ltd. All rights reserved.