The paper is devoted to an algorithm for computing matrices and for a given square matrix and a real . The algorithm uses the binary expansion of and has the logarithmic computational complexity with respect to . The problem stems from the control theory.
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
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