Successive eigenvalue relaxation: A new method for the generalized eigenvalue problem and convergence estimates (Q2748134)

The slightly more than 10 pages of this paper form an archetype presentation (of a method) with a marvelously composed title (which is openly and almost exhaustively descriptive) and using a high-brow style (which is not quite usual, using citation in Greek and framing the text between strongly philosophical ``prolegomena'' and exceptionally enthusiastic ``epilegomena''). In this spirit the authors combine the extensive historical review with the Draconian selection of the material itself (referring, e.g., to the proofs published separately in two reports, or omitting the explicit formulae from theorems in order to maximize the simplicity of the message). NEWLINENEWLINENEWLINESomebody may like the maximal digestibility of the resulting text. I would be more sceptical -- the idea itself (iterations in subspaces plus a convergence estimate) is nice and verbally ambitious (we read that it does not require any information about the preconditioner used) but the ``proof of the pudding'' may look like missing (the promised ``effective dealing with large-scale eigenvalue problems'' is consummated via the mere single two-dimensional Laplacean-like numerical illustration). Hence, I would personally wait with the evaluation of the recommended successive eigenvalue relaxation (SER) method until the above-mentioned two internal reports of the University of Westminster appear in print (it is really difficult not to accept and mimic the style, so let me add, in this spirit, a small fraction from a poem by Pablo Neruda, in Spanish: ``Primero vivo, \dots{} despues video que pueda SER'').