We propose a method and algorithm for computing the weighted Moore-Penroseinverse of one-variable rational matrices. Continuing this idea, we develop analgorithm for computing the weighted Moore-Penrose inverse of one-variablepolynomial matrix. These methods and algorithms are generalizations of themethod for computing the weighted Moore-Penrose inverse for constant matrices,originated in Wang and Chen [G.R. Wang, Y.L. Chen, A recursive algorithm forcomputing the weighted Moore-Penrose inverse AMN, J. Comput. Math. 4 (1986)74-85], and the partitioning method for computing the Moore-Penrose inverse ofrational and polynomial matrices introduced in Stanimirovic and Tasic [P.S.Stanimirovic, M.B. Tasic, Partitioning method for rational and polynomialmatrices, Appl. Math. Comput. 155 (2004) 137-163]. Algorithms are implementedin the symbolic computational package MATHEMATICA.
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