Article

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

Applied Mathematics and Computation (Impact Factor: 1.35). 01/2011; DOI: 10.1016/j.amc.2011.04.080

Source: arXiv

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**ABSTRACT:**In this letter, we propose a novel iterative method for computing generalized inverse, based on a novel KKT formulation. The proposed iterative algorithm requires making four matrix and vector multiplications at each iteration and thus has low computational complexity. The proposed method is proved to be globally convergent without any condition. Furthermore, for fast computing generalized inverse, we present an acceleration scheme based on the proposed iterative method. The global convergence of the proposed acceleration algorithm is also proved. Finally, the effectiveness of the proposed iterative algorithm is evaluated numerically.Neural Computation 02/2014; 26(2):449–465. · 1.76 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this work we study a minimization problem for a matrix-valued function under linear constraints, in the case of a singular matrix. The proposed method differs from others on the restriction of the minimizing matrix to the range of the corresponding quadratic function. Moreover, we present two applications of the proposed minimization method in Linear Regression and B-spline smoothing.Journal of Applied Mathematics and Computing 01/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**A third order iterative method for estimating the Moore-Penrose generalised inverse is developed by extending the second order iterative method described in Petkovi and Stanimirovi 2011. Convergence analysis along with the error estimates of the method are investigated. Three numerical examples, two for full rank simple and randomly generated singular rectangular matrices and third for rank deficient singular square matrices with large condition numbers from the matrix computation toolbox are worked out to demonstrate the efficacy of the method. The performance measures used are the number of iterations and CPU time used by the method. On comparing the results obtained by our method with those obtained with the method given in Petkovi and Stanimirovi 2011, it is observed that our method gives improved performance.International Journal of Computing Science and Mathematics 01/2013; 4.2:140-151.

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