Simplification and Accurate Implementation of State Evolution Recursion for Conjugate Gradient

摘要

This letter simplifies and analyze existing state evolutionrecursions for conjugate gradient. The proposed simplification reduces thecomplexity for solving the recursions from cubic order to square order inthe total number of iterations. The simplified recursions are still catastrophicallysensitive to numerical errors, so that arbitrary-precision arithmetic isused for accurate evaluation of the recursions.