## 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

## 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

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## Additional Information

- © Copyright 1992 American Mathematical Society
- 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