Symmetric Matrix Polynomial Equation
نویسنده
چکیده
A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it is numerically reliable. It results in a simple characterization of all solutions of expected column degrees. Several new theoretical results concerning stability theory and reduced Sylvester resultant matrices are also developed in parallel and used to conclude a priori on the existence of a solution. Finally some basic examples illustrate the simplicity of the numerical method.
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