Report Number: CS-TR-66-45
Institution: Stanford University, Department of Computer Science
Title: Relaxation methods for semi-definite systems
Author: Kahan, William
Date: August 1966
Abstract: Certain non-stationary relaxation iterations, which are commonly applied to positive definite symmetric systems of linear equations, are also applicable to a semi-definite system provided that system is consistent. Some of the convergence theory of the former application is herein extended to the latter application. The effects of rounding errors and of inconsistency are discussed too, but with few helpful conclusions. Finally, the application of these relaxation iterations to an indefinite system is shown here to be ill-advised because these iterations will almost certainly diverge exponentially.
http://i.stanford.edu/pub/cstr/reports/cs/tr/66/45/CS-TR-66-45.pdf