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(Reference retrieved automatically from SciELO through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Reginaldo J. Santos [1] ; Álvaro R. de Pierro [2]
Total Authors: 2
Affiliation:
[1] Universidade Federal de Minas Gerais. ICEx. Departamento de Matemática - Brasil
[2] State University of Campinas. IMECC. Department of Applied Mathematics - Brasil
Total Affiliations: 2
Document type: Journal article
Source: COMPUTATIONAL & APPLIED MATHEMATICS; v. 25, n. 1, p. 111-128, 2006-00-00.
Abstract

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. (AU)

FAPESP's process: 02/07153-2 - Algorithms for tomographic reconstruction: optimization, restoration, quantification and clinical application
Grantee:Sergio Shiguemi Furuie
Support Opportunities: Research Projects - Thematic Grants