Report Number: CS-TR-68-88
Institution: Stanford University, Department of Computer Science
Title: Relaxation methods for convex problems
Author: Schechter, Samuel
Date: February 1968
Abstract: Extensions and simplifications are made for convergence
proofs of relaxation methods for nonlinear systems arising
from the minimization of strictly convex functions. This work
extends these methods to group relaxation, which includes an
extrapolated form of Newton's method, for various orderings.
A relatively simple proof is given for cyclic orderings,
sometimes referred to as nonlinear overrelaxation, and for
residual orderings where an error estimate is given. A less
restrictive choice of relaxation parameter is obtained than
that previously. Applications are indicated primarily to the
solution of nonlinear elliptic boundary problems.