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Persistent URL http://purl.org/net/epubs/work/62129
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Record Id 62129
Title Linear regression models, least-squares problems, and stopping criteria for the conjugate gradient method
Abstract Minimum-variance unbiased estimates for linear regression models can be obtained by solving least-squares problems. The Conjugate Gradient method can be successfully used in solving the symmetric and positive definite normal equations obtained from these least-squares problems. Taking into account the results of [9, 10, 13, 25], which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process, we adapt the stopping criterion introduced in [2] to the normal equations taking into account the statistical properties of the underpinning linear regression problem. Moreover, we show how the energy norm of the error is linked 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 problems , Linear regression , sparse matrices
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Language English (EN)
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Journal Article Comp Phys Commun 183, no. 11 (2012): 2322-2336. doi:10.1016/j.cpc.2012.05.023 2012