Elementary Divisors of the Liebmann Process
G. A. Miles, K. L. Stewart, Garry J. Tee · The Computer Journal · 1964
When the Liebmann process is applied (with pagewise ordering) to the finite-difference Dirichlet problem for Poisson's equation within a rectangle, the multiple zero eigenvalue of the process is associated with non-linear elementary divisors. The eigenvectors with zero eigenvalue are constructed explicitly, and bounds are deduced for the number of iterations which are needed to annihilate all components of the initial error which are associated with zero eigenvalues.