Resumo

SANTOS, Reginaldo J.  e  PIERRO, Álvaro R. de. The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography. Comput. Appl. Math. [online]. 2006, vol.25, n.1, pp. 111-128. ISSN 1807-0302.

We study the effect of the nonlinear dependence of the iterate x^k 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 x^k 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.

Palavras-chave : Generalized Cross Validation; Tomography; Conjugate Gradients.