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Abstract
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In this paper, an algorithm is proposed to compute the inverse of
an invertible matrix. The new algorithm is a generalization of the
algorithms based on the well-known Schultz-type iterative methods. We show that the convergence order of the new method is a linear combination of the Fibonacci sequence and also is powerful
and efficient in finding and keeping sparsity of the obtained approximate inverse of sparse matrices. The convergence of the algorithm is analysed and some applications are studied. It is shown that the
proposed algorithm can be used for computing an approximation of
the Moore–Penrose inverse of matrices. Numerical examples are provided to verify the feasibility and effectiveness of the new method.
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