Abstract
The implementation of the Preconditioned Conjugate Gradient method for the solution of large linear systems arising from the discretization of differential operators, requires the pre-determination of only one iteration parameter. The numerical determination of the optimal value of this constant parameter, involves the spectral bounds of some matrices and can be obtained in O ( N 2 ) sine function evaluations, where 1/ N is the discretization mesh size. It is shown that this parameter can be chosen in a stable manner in O (1) operations per iteration, if it is allowed to vary with the iteration index from information derived from the gradient parameters.
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