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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Regularization and the general Gauss-Markov linear model

Authors: Hong Yuan Zha and Per Christian Hansen
Journal: Math. Comp. 55 (1990), 613-624
MSC: Primary 65F20; Secondary 15A06, 65F30
MathSciNet review: 1035946
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Abstract: If the coefficient matrix in the general Gauss-Markov linear model is ill-conditioned, then the solution is very sensitive to perturbations. For such problems, we propose to add Tikhonov regularization to the model, and we show that this actually stabilizes the solution and decreases its variance. We also give a numerically stable algorithm for computing the regularized solution efficiently.

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Keywords: Estimation in the general Gauss-Markov linear model, Tikhonov regularization, restricted SVD, discrete Picard condition
Article copyright: © Copyright 1990 American Mathematical Society