论文信息 - A Rapid Numerical Algorithm to Compute Matrix Inversion

A Rapid Numerical Algorithm to Compute Matrix Inversion

The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.

Fazlollah Soleymani | F. Soleymani

[1] Edmond Chow,et al. Approximate Inverse Preconditioners via Sparse-Sparse Iterations , 1998, SIAM J. Sci. Comput..

[2] Takashi Nodera,et al. A new scheme of computing the approximate inverse preconditioner for the reduced linear systems , 2007 .

[3] Weiguo Li,et al. A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix , 2010, Appl. Math. Comput..

[4] E. V. Krishnamurthy,et al. Numerical algorithms : computations in science and engineering , 2008 .

[5] Davod Khojasteh Salkuyeh,et al. On the Relation between the AINV and the FAPINV Algorithms , 2009, Int. J. Math. Math. Sci..

[6] M. Denham,et al. The mathematica book: Stephen Wolfram. Wolfram Media/Cambridge University Press, 3rd edition (1996) , 1997 .

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

[8] Michele Benzi,et al. Numerical experiments with two approximate inverse preconditioners , 1998 .

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

[10] Mei Han An,et al. accuracy and stability of numerical algorithms , 1991 .

[11] Victor Y. Pan,et al. Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices , 2004, Numerical Algorithms.

[12] Victor Y. Pan,et al. An Improved Newton Iteration for the Generalized Inverse of a Matrix, with Applications , 1991, SIAM J. Sci. Comput..