Fast Moving Window Algorithm for QR and Cholesky Decompositions

W. Liang; U. Kruger; X. Wang; L. Xie; Timothy Littler

doi:10.3182/20080706-5-KR-1001.01710

Fast Moving Window Algorithm for QR and Cholesky Decompositions

W. Liang, U. Kruger, X. Wang, L. Xie, Timothy Littler

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

Original language	English
Title of host publication	Proceedings of the 17th IFAC World Congress (IFAC '06)
Pages	10106-10111
Number of pages	6
DOIs	https://doi.org/10.3182/20080706-5-KR-1001.01710
Publication status	Published - Jul 2008
Event	17th World Congress of the International Federation of Automatic Control 2008 - Seoul, Korea, Republic of Duration: 01 Jul 2008 → 01 Jul 2008

Conference

Conference	17th World Congress of the International Federation of Automatic Control 2008
Abbreviated title	IFAC 2008
Country/Territory	Korea, Republic of
City	Seoul
Period	01/07/2008 → 01/07/2008

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10.3182/20080706-5-KR-1001.01710

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title = "Fast Moving Window Algorithm for QR and Cholesky Decompositions",

abstract = "This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers{\textquoteright} approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.",

author = "W. Liang and U. Kruger and X. Wang and L. Xie and Timothy Littler",

year = "2008",

month = jul,

doi = "10.3182/20080706-5-KR-1001.01710",

language = "English",

pages = "10106--10111",

booktitle = "Proceedings of the 17th IFAC World Congress (IFAC '06)",

note = "17th World Congress of the International Federation of Automatic Control 2008, IFAC 2008 ; Conference date: 01-07-2008 Through 01-07-2008",

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T1 - Fast Moving Window Algorithm for QR and Cholesky Decompositions

AU - Liang, W.

AU - Kruger, U.

AU - Wang, X.

AU - Xie, L.

AU - Littler, Timothy

PY - 2008/7

Y1 - 2008/7

N2 - This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

AB - This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

U2 - 10.3182/20080706-5-KR-1001.01710

DO - 10.3182/20080706-5-KR-1001.01710

M3 - Conference contribution

SP - 10106

EP - 10111

BT - Proceedings of the 17th IFAC World Congress (IFAC '06)

T2 - 17th World Congress of the International Federation of Automatic Control 2008

Y2 - 1 July 2008 through 1 July 2008

ER -

Fast Moving Window Algorithm for QR and Cholesky Decompositions

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