The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography

We study the effect of the nonlinear dependence of the iterate xk of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate xk depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion.

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