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Factorizations of hyperpower family of iterative methods via least squares approach. (English) Zbl 1416.65104

Summary: A new method for finding proper factorizations of the hyperpower family of iterative methods for computing generalized inverses is proposed. The method is based on numerical optimization of an appropriate least squares problem. An iterative method in a non-normalized form for finding the generalized outer inverses with prescribed range and null space of any given complex matrix is proposed and considered. Computational complexity and convergence of the method are studied. Several numerical experiments are also presented.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A09 Theory of matrix inversion and generalized inverses
15A23 Factorization of matrices

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