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

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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

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SIAM Journal on Matrix Analysis and Applications, 40(1), 235–253, 2019 BibTeX reference