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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Error analysis of $ QR$ updating with exponential windowing


Author: G. W. Stewart
Journal: Math. Comp. 59 (1992), 135-140
MSC: Primary 65F25; Secondary 65G05
MathSciNet review: 1134738
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Abstract: Exponential windowing is a widely used technique for suppressing the effects of old data as new data is added to a matrix. Specifically, given an $ n \times p$ matrix $ {X_n}$ and a "forgetting factor" $ \beta \in (0,1)$, one works with the matrix $ {\operatorname{diag}}({\beta ^{n - 1}},{\beta ^{n - 2}}, \ldots ,1){X_n}$. In this paper we examine an updating algorithm for computing the QR factorization of $ {\operatorname{diag}}({\beta ^{n - 1}},{\beta ^{n - 2}}, \ldots ,1){X_n}$ and show that it is unconditionally stable in the presence of rounding errors.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1134738-1
PII: S 0025-5718(1992)1134738-1
Article copyright: © Copyright 1992 American Mathematical Society