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.

在本文中，发展了有理矩阵的广义逆的新颖表示。因此，考虑了用于计算给定矩阵A的{1,2,3}和{1,2,4}逆和Moore-Penrose逆的统一方法。利用有理矩阵的全秩QDR分解来避免评估中有理表达式的平方根，从而使给定算法非常适合于广义矩阵逆的符号计算。此外，我们开发了一种算法，该算法使用满秩QDR分解对多项式矩阵的Moore-Penrose逆进行符号计算，从而最大程度地利用了无平方根多项式项的潜力。通过数值示例说明了引入的算法。