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# Error Analysis of QR Updating with Exponential Windowing

G. W. Stewart
Mathematics of Computation
Vol. 59, No. 199 (Jul., 1992), pp. 135-140
DOI: 10.2307/2152984
Stable URL: http://www.jstor.org/stable/2152984
Page Count: 6
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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 × p matrix Xn and a "forgetting factor" β ∈ (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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