ON THE RATE OF CONVERGENCE OF THE CONJUGATE GRADIENT METHOD FOR LINEAR OPERATORS IN HILBERT SPACE
Owe Axelsson, János Karátson · Numerical Functional Analysis and Optimization · 2002
The rate of convergence of the conjugate gradient method is investigated in Hilbert space. Previous results in R n for the sublinear and superlinear rate of convergence, involving various generalized condition numbers, are extended to linear operators. Applications are given to elliptic differential operators, yielding relevant mesh independent estimates including large matrix sizes in the case of discretized boundary value problems.