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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
DOI: https://doi.org/10.1090/S0025-5718-1992-1134738-1
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.


References [Enhancements On Off] (What's this?)

  • Gene H. Golub and Charles F. Van Loan, Matrix computations, 2nd ed., Johns Hopkins Series in the Mathematical Sciences, vol. 3, Johns Hopkins University Press, Baltimore, MD, 1989. MR 1002570
  • G. W. Stewart, An updating algorithm for subspace tracking, Technical Report CS-TR 2494, Department of Computer Science, Univ. of Maryland, 1990 (to appear in IEEE Trans. Acoust. Speech Signal Process.).
  • G. W. Stewart, Updating a rank-revealing $ULV$ decomposition, SIAM J. Matrix Anal. Appl. 14 (1993), no. 2, 494–499. MR 1211802, DOI https://doi.org/10.1137/0614034
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Article copyright: © Copyright 1992 American Mathematical Society