Talk:Iterative refinement

I suspect the error analysis of having implicit assumptions, or else being very slack. In particular it does not depend on the method for the solution of Ax=b, and assumes convergence. Jdh41 (talk) 10:01, 21 July 2009 (UTC)

This page needs notes on the convergence analysis added. See Skeel (1980) or Arioli, Demmel and Duff (1988). Jdh41 (talk) 10:01, 21 July 2009 (UTC)

You're right. An assumption mentioned by Moler was left out, which says each iteration satisfies

${\boldsymbol {A}}({\boldsymbol {I}}+{\boldsymbol {F}}_{m}){\boldsymbol {d}}_{m}={\boldsymbol {r}}_{m}$

where $\lVert {\boldsymbol {F}}_{m}\rVert <1$. This means that solve step should always be reasonably accurate.Kxx (talk) 18:30, 25 July 2009 (UTC)