RRQR factorization

An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine the rank of a matrix.^[1] The singular value decomposition can be used to generate an RRQR, but it is not an efficient method to do so.^[2] An RRQR implementation is available in MATLAB.^[3]

References

^ Gu, Ming; Stanley C. Eisenstat (July 1996). "Efficient algorithms for computing a strong rank-revealing QR factorization" (PDF). SIAM Journal on Scientific Computing. 17 (4): 848–869. Bibcode:1996SJSC...17..848G. doi:10.1137/0917055. Retrieved 22 September 2014.
^ Hong, Y.P.; C.-T. Pan (January 1992). "Rank-Revealing QR Factorizations and the Singular Value Decomposition". Mathematics of Computation. 58 (197): 213–232. doi:10.2307/2153029. JSTOR 2153029.
^ "RRQR Factorization" (PDF). 29 March 2007. Archived from the original (PDF) on 14 May 2011. Retrieved 2 April 2011.

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[GuSciComput1996-1] Gu, Ming; Stanley C. Eisenstat (July 1996). "Efficient algorithms for computing a strong rank-revealing QR factorization" (PDF). SIAM Journal on Scientific Computing. 17 (4): 848–869. Bibcode:1996SJSC...17..848G. doi:10.1137/0917055. Retrieved 22 September 2014.

[HongPan92-2] Hong, Y.P.; C.-T. Pan (January 1992). "Rank-Revealing QR Factorizations and the Singular Value Decomposition". Mathematics of Computation. 58 (197): 213–232. doi:10.2307/2153029. JSTOR 2153029.

[RRQR_Factorization_MATLAB_Docs-3] "RRQR Factorization" (PDF). 29 March 2007. Archived from the original (PDF) on 14 May 2011. Retrieved 2 April 2011.

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v t e Numerical linear algebra
Key concepts	Floating point Numerical stability
Problems	System of linear equations Matrix decompositions Matrix multiplication (algorithms) Matrix splitting Sparse problems
Hardware	CPU cache TLB Cache-oblivious algorithm SIMD Multiprocessing
Software	ATLAS MATLAB Basic Linear Algebra Subprograms (BLAS) LAPACK Specialized libraries General purpose software

RRQR factorization

RRQR factorization

RRQR factorization

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RRQR factorization

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