Elizabeth H. Cuthill and Richard S. Varga, A method of normalized block iteration, J. Assoc. Comput. Math. 6 (1959), 236-244. MR 22, 8651. Zbl. 88, p. 94.

1. Introduction

The Young-Frankel successive point overrelaxation scheme [14,4] has been
shown [14] to be applicable in solving partial difference equations of elliptic
type arising from discrete approximations to general partial differential
equations of elliptic type. More recently, Arms, Gates, and Zondek [1]
generalized the successive point overrelaxation scheme of Young-Frankel to what
is called the successive block overrelaxation scheme, and they stated that, with
certain additional assumptions, a theoretical advantage in the rates of
convergence is always obtained in using successive block overrelaxation rather
than successive point overrelaxation. In particular, for the numerical solution
of the Dirichlet problem of uniform mesh size *h* in a rectangle, the
successive block overrelaxation scheme [1] is asymptotically faster by a factor
of 2^{1/2} than the successive point overrelaxation shceme, as *h -->
0*. Despite that advantage, the successive block overrelaxation scheme has
not been widely used, mainly because the usual computing machine application of
block overrelaxation requires more arithmetic operations than point
overrelaxation, and this increase in the number of arithmetic operations would
appear to cancel any gains in the rates of convergence.