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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Error analysis of $QR$ updating with exponential windowing
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by G. W. Stewart PDF
Math. Comp. 59 (1992), 135-140 Request permission


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.
  • 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.Β 2, 494–499. MR 1211802, DOI 10.1137/0614034
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 135-140
  • MSC: Primary 65F25; Secondary 65G05
  • DOI:
  • MathSciNet review: 1134738