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 , , where and are arbitrary complex matrices and is the residual . The authors examine the method with residual modified to , with idempotent.
The main thrust of the paper is analysis of the convergence of for some , where will be related to the matrices defined previously. If the basic iteration converges, an appropriate and limit have to be found and the paper discusses such possibilities.