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The hyperpower iteration revisited. (English) Zbl 0848.65021

This paper discusses an extension of the hyperpower method [cf. A. Ben-Israel, Math. Comput. 19, 452-455 (1965; Zbl 0136.12703)], which may be used for iterative computation of generalised inverses for example. The hyperpower method uses a basic iteration X k+1 =X k (I+R k ++R k q-1 ), q2, where A and X 0 are arbitrary complex matrices and R k is the residual I-AX k . The authors examine the method with residual modified to P(I-AX k ), with P idempotent.

The main thrust of the paper is analysis of the convergence of B q k for some B n×n , where B will be related to the matrices defined previously. If the basic iteration converges, an appropriate P and limit L have to be found and the paper discusses such possibilities.

65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65F10Iterative methods for linear systems
15A09Matrix inversion, generalized inverses