Generalized inverses in block designs (Q1071448)

The Kuiper-Corsten iteration is a well-known method of iteratively solving the normal equations for the treatment parameters arising from a designed block experiment. It can be used as an iterative method of calculating \textit{K. D. Tocher}'s \(\Omega\) [J. R. Stat. Soc., Ser. B 14, 45-100 (1952; Zbl 0047.379)], which is a generalized inverse of the matrix involved in the normal equations. Other choices of generalized inverse have been proposed, for example \textit{S. C. Pearce}'s \(\Theta\) [Biometr. Z. 18, 105-116 (1976; Zbl 0329.62061)], with corresponding iterative formulae. We present an approach which leads to a class of generalized inverses containing those mentioned. It extends previous results, clarifies the relation between them, and stresses their connection with the Moore- Penrose inverse.