Alternative to the svd: Rank revealing qr-factorizations

Tony F. Chan

doi:10.1117/12.936872

Alternative to the svd: Rank revealing qr-factorizations

Tony F. Chan^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

5 Citations (Scopus)

Abstract

Both the singular value decomposition (SVD) and the QR factorization play central roles in signal processing algorithms. The usual tradeoff is that the SVD is more expensive but can reveal rank more reliably. In this paper, we show how to construct a QR factorization which can also reveal the rank reliably. For matrices with low rank deficiency, the overhead over the usual QR procedures is negligible. It also appears possible to implement the new procedure in systolic arrays.

Original language	English
Pages (from-to)	31-38
Number of pages	8
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	696
DOIs	https://doi.org/10.1117/12.936872
Publication status	Published - 4 Apr 1986
Externally published	Yes

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title = "Alternative to the svd: Rank revealing qr-factorizations",

abstract = "Both the singular value decomposition (SVD) and the QR factorization play central roles in signal processing algorithms. The usual tradeoff is that the SVD is more expensive but can reveal rank more reliably. In this paper, we show how to construct a QR factorization which can also reveal the rank reliably. For matrices with low rank deficiency, the overhead over the usual QR procedures is negligible. It also appears possible to implement the new procedure in systolic arrays.",

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AB - Both the singular value decomposition (SVD) and the QR factorization play central roles in signal processing algorithms. The usual tradeoff is that the SVD is more expensive but can reveal rank more reliably. In this paper, we show how to construct a QR factorization which can also reveal the rank reliably. For matrices with low rank deficiency, the overhead over the usual QR procedures is negligible. It also appears possible to implement the new procedure in systolic arrays.

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JF - Proceedings of SPIE - The International Society for Optical Engineering

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Alternative to the svd: Rank revealing qr-factorizations

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