An algorithmic technique for the investigation of the non-negativity (or positivity) of a homogeneous matrix pencil
In the classical literature of matrix pencils theory, the dual pencils sF - G and F - (s) over capG are identified by the homogeneous matrix pencil sF - (s) over capG, where s, (s) over cap are indeterminates. In the present paper, we discuss and we provide a characterization of the nonnegativity (or positivity) of a given homogeneous pencil. An algorithmic approach for the analytic determination of all the nonnegative (or positive) homogeneous pencils into a relevant set of indeterminates s, (s) over cap is provided. This new approach can be easily transferred into a standard computational routine by using simple Matlab m-files. Some numerical examples are also concluded.
matrix pencil theory algorithmic approach nonnegativity (positivity)