We propose a method and algorithm for computing the weighted Moore-Penrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method or computing the weighted Moore-Penrose inverse for constant matrices, originated in [28], and the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in [23]. Algorithms are implemented in the symbolic computational package MATHEMATICA.Corresponding algorithms for two-variable polynomial matrices are introduced in [27]. These algorithms are efficient when the input matrix is dense. C) Grevile's partitioning method for numerical computation of generalized inverses is introduced in [7]. Two different proofs for Greville's method were presented in [4], [29]. A simple derivation of the Grevile's result has been given by Udwadia and Kalaba [26]. In [8] Fan and Kalaba used the approach of determination of the Moore-Penrose inverse of matrices using dynamic programming and Belman's principle of optimality. Wang in [28] generalizes Grevile's method to the weighted Moore-Penrose inverse. Also, the results in [28] are proved using a new technique.In [21] the Greville's algorithm is estimated as the method which needs more operations and consequently it accumulates more rounding errors. Moreover, it is well-known that the Moore-Penrose inverse is not necessarily a continuous function of the elements of the matrix. The existence of this discontinuity present further problems in the pseudoinverse computation. It is therefore clear that cumulative round off errors should be totally eliminated. During the symbolic implementation, variables are stored in the "exact" form or can be left "unassigned" (without numerical values), resulting in no loss of accuracy during the calculation [12].An algorithm for computing the Moore-Penrose inverse of one-variable polynomial and/or rational matrices, based on the Grevile's partitioning algorithm, was introduced in [23]. An extension of results from [23] to the set of twovariable rational and polynomial matrices is introduced in the paper [19].In the present paper we extend Wang's partition method from [28] to the set of one-variable rational and polynomial matrices. In this way, we obtain an algorithm for computing the weighted Moore-Penrose inverse of one-variable rational and polynomial matrices. The paper is a generalization of the paper [28] and a continuation of the paper [23].The structure of the paper is as follows. In the second section we extend the algorithm for computing the weighted Moore-Penrose from [28] to the set of one-variable rational matrices. In Section 3 we give the main theorem and adapt this algorithm to the set of polynomial matrices. Several symbolic examples are arranged in fourth section. In partial case M = I m , N = I n we obtain the usual Moore-Penrose inverse, and then use test examples from [32]. ...

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An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse

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The main aim of this paper is to develop a client/server-based model for computing the weighted Moore-Penrose inverse using the partitioning method as well as for storage of generated results. The web application is developed in the PHP/MySQL environment. The source code is open and free for testing by using a web browser. Influence of different matrix representations and storage systems on the computational time is investigated. The CPU time for searching the previously stored pseudo-inverses is compared with the CPU time spent for new computation of the same inverses.