Error Analysis of QR Updating with Exponential Windowing
Error Analysis of QR Updating with Exponential Windowing
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Date
1998-10-15
Authors
Stewart, G. W.
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Abstract
To appear in Mathematics of Computation
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
$\dia(\beta^{n-1},\beta^{n-2},\ldots,1)X_n$. In this paper we
examine an updating algorithm for computing the QR factorization of
$\dia(\beta^{n-1},\beta^{n-2},\ldots,1)X_n$ and show that it is
unconditionally stable in the presence of rounding errors.
(Also cross-referenced as UMIACS-TR-91-79)