Abstract
In this paper, novel representations of generalized inverses of rational matrices are developed. Therefore, a unified approach for the computation of {1,2,3} and {1,2,4} inverses and Moore-Penrose inverse of a given matrix A is considered. Full-rank QDR decomposition of a rational matrix is utilized to avoid the square roots of rational expressions in the evaluations, making the given algorithm very suitable for symbolic computations of generalized matrix inverses. Furthermore, we developed an algorithm for symbolic computation of the Moore-Penrose inverse of a polynomial matrix using the full-rank QDR decomposition, therefore maximizing the potential of using square root–free polynomial entries. Introduced algorithms are illustrated via numerical examples.
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Funding
Ivan P. Stanimirović and Milan Tasić received support from the Research Project 174013 of the Serbian Ministry of Science.
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Aldhafeeri, N., Pappas, D., Stanimirović, I.P. et al. Representations of generalized inverses via full-rank QDR decomposition. Numer Algor 86, 1327–1337 (2021). https://doi.org/10.1007/s11075-020-00935-4
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DOI: https://doi.org/10.1007/s11075-020-00935-4