Finding generalized inverses by a fast and efficient numerical method

In this paper, a method with very high order of convergence is constructed and analyzed. The method is used to compute generalized inverses. The efficiency index has been employed to show its superiority. Numerical experiments re-verify that the proposed iterative expression is more effective than the existing methods of the same type.

[1]  Xiaoji Liu,et al.  A High-Order Iterate Method for Computing A(2)T, S , 2014, J. Appl. Math..

[2]  Predrag S. Stanimirovic,et al.  Full-rank representations of outer inverses based on the QR decomposition , 2012, Appl. Math. Comput..

[3]  Adi Ben-Israel,et al.  An iterative method for computing the generalized inverse of an arbitrary matrix , 1965 .

[4]  Xiaoji Liu,et al.  Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices , 2013 .

[5]  Fazlollah Soleymani,et al.  On finding robust approximate inverses for large sparse matrices , 2014 .

[6]  Yong Zhang,et al.  Chebyshev-type methods and preconditioning techniques , 2011, Appl. Math. Comput..

[7]  Liu Weiguo,et al.  A family of iterative methods for computing Moore–Penrose inverse of a matrix , 2013 .

[8]  Predrag S. Stanimirovic,et al.  A class of numerical algorithms for computing outer inverses , 2014, J. Comput. Appl. Math..

[9]  Michael Trott.  The Mathematica GuideBook for Numerics , 2005 .

[10]  Bing Zheng,et al.  Representation and approximation for generalized inverseAT,S(2): Revisited , 2006 .

[11]  Fazlollah Soleymani,et al.  Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse , 2014, J. Appl. Math..

[12]  Predrag S. Stanimirovic,et al.  An accelerated iterative method for computing weighted Moore-Penrose inverse , 2013, Appl. Math. Comput..

[13]  Joan-Josep Climent,et al.  A geometrical approach on generalized inverses by Neumann-type series , 2001 .

[14]  G. Schulz.  Iterative Berechung der reziproken Matrix , 1933 .

[15]  Predrag S. Stanimirovic,et al.  A note on the stability of a pth order iteration for finding generalized inverses , 2014, Appl. Math. Lett..

[16]  Predrag S. Stanimirović,et al.  A Higher Order Iterative Method for Computing the Drazin Inverse , 2013, TheScientificWorldJournal.

[17]  Higher-Order Convergent Iterative Method for Computing the Generalized Inverse over Banach Spaces , 2013 .