Report Number: CS-TR-72-304
Institution: Stanford University, Department of Computer Science
Title: Richardson's non-stationary matrix iterative procedure.
Author: Anderssen, Robert S.
Author: Golub, Gene H.
Date: August 1972
Abstract: Because of its simplicity, Richardson's non-stationary
iterative scheme is a potentially powerful method for the
solution of (linear) operator equations. However, its general
application has more or less been blocked by
(a) the problem of constructing polynomials, which deviate
least from zero on the spectrum of the given operator, and
which are required for the determination of the iteration
parameters of the non-stationary method, and
(b) the instability of this scheme with respect to rounding
Recently, these difficulties were examined in two Russian
papers. In the first, Lebedev  constructed polynomials
which deviate least from zero on a set of subintervals of the
real axis which contains the spectrum of the given operator.
In the second, Lebedev and Finogenov  gave an ordering
for the iteration parameters of the non-stationary Richardson
scheme which makes it a stable numerical process. Translation
of these two papers appear as Appendices 1 and 2,
respectively, in this report. The body of the report
represents an examination of the properties of Richardson's
non-stationary scheme and the pertinence of the two mentioned
papers along with the results of numerical experimentation
testing the actual implementation of the procedures given in