A Note on the Generalized Conjugate Gradient Method
Stanley C. Eisenstat · SIAM Journal on Numerical Analysis · 1983
Each iterate generated by the Generalized Conjugate Gradient method of Concus and Golub [Lecture Notes in Economics and Mathematical Systems 134, Springer-Verlag, New York, 1976] and Widlund [SIAM J. Numer. Anal., 15 (1978), pp. 801–812] is shown to be the best approximation to the solution from a certain affine subspace (although not from the “natural” afline Krylov subspace). This property is used to improve the error bounds given by Widlund and Hageman, Luk and Young [SIAM J. Numer. Anal., 17 (1980), pp. 852–873].