An improved method for the computation of the Moore–Penrose inverse matrix

Applied Mathematics and Computation (Impact Factor: 1.55). 08/2011; DOI: 10.1016/j.amc.2011.04.080
Source: arXiv

ABSTRACT In this article we provide a fast computational method in order to calculate the Moore–
Penrose inverse of singular square matrices and of rectangular matrices. The proposed
method proves to be much faster and has significantly better accuracy than the already
proposed methods, while works for full and sparse matrices.

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Available from: Vasilios N Katsikis, Sep 26, 2015
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    • "where ψ † k is the pseudoinverse or the Moore–Penrose inverse [40] of ψ k . Equation (12) can also be solved by the recursive least squares method [41]. "
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    • "Therefore the only parameters that should be learned are weights between the hidden layer and the output layer. The pseudo inverse method that is fast algorithm and does not fall into a local minimum is used for computing the weights between the hidden layer and the output one [8].Efficient algorithms for computing pseudo inverse methods are discussed in [11] [12]. In this case the number of hidden layer neurons is determined experimentally. "
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    • "[9], a method (qrginv) for computing the Moore-Penrose inverse of an arbitrary matrix was presented. They made use of the QR-factorization, as well as an algorithm based on a known reverse order law for generalized inverse matrices, and also they apply a method (ginv), presented in [4], based on a full rank Cholesky factorization of possibly singular symmetric positive matrices. "
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    ABSTRACT: Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an real matrix A with rank . Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.
    01/2014; 2014:1-5. DOI:10.1155/2014/641706
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