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DOI 10.5286/raltr.2008008
Persistent URL http://purl.org/net/epubs/work/50391
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Record Id 50391
Title Least-squares problems, normal equations, and stopping criteria for the conjugate gradient method
Abstract The Conjugate Gradient method can be successfully used in solving the symmetric and positive definite normal equations obtained from least-squares problems. Taking into account the results of Hestenes and Stiefel (1952), Golub and Meurant (1997), and Strakoˇs and Tichy (2002), which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process, we adapt the stopping criterion introduced by Arioli (2005). Moreover, we show how the energy norm of the error is linked to the statistical properties of the least-squares problem and to the χ2-distribution and to the Fisher-Snedecor distribution. Finally, we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criteria.
Organisation CSE , CSE-NAG , STFC
Keywords Stopping criteria , Conjugate gradient , Least squares problem , Linear regression
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-008. STFC, 2008. RALTR2008008.pdf 2008