Multiple Recursion Conjugate Gradient Algorithms Part I: Sufficient Conditions
Teri Barth, Thomas A. Manteuffel · SIAM Journal on Matrix Analysis and Applications · 2000
In this paper we show that a conjugate gradient method can be implemented using a short multiple recursion for a wider class of matrices than that demonstrated by Faber and Manteuffel [ SIAM J. Numer. Anal., 21 (1984), pp. 352--362]. In part I of this paper, sufficient conditions are determined in order that a conjugate gradient method can be implemented using this form of multiple recursion. Part II of this paper addresses necessary conditions. This is the first known short recursion for a conjugate gradient method that can be applied to a nonnormal matrix of nontrivial degree.