Group for Research in Decision Analysis

G-2016-70

Estimates of the 2-norm forward error for SYMMLQ and CG

, , and

For positive definite linear systems (or semidefinite consistent systems), we use Gauss-Radau quadrature to obtain a cheaply computable upper bound on the 2-norm error of SYMMLQ iterates. The close relationship between SYMMLQ and CG iterates lets us construct an upper bound on the 2-norm error for CG. For indefinite systems, the upper bound becomes an estimate of the 2-norm SYMMLQ error. Numerical experiments demonstrate that the bounds and estimates are remarkably tight.

, 15 pages