RRQR factorization

{{Short description|Concept in linear algebra}}

{{Use dmy dates|date=February 2022}}

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.{{cite journal|last=Gu|first=Ming|author2=Stanley C. Eisenstat |title=Efficient algorithms for computing a strong rank-revealing QR factorization|journal=SIAM Journal on Scientific Computing|date=July 1996|volume=17|issue=4|pages=848–869|doi=10.1137/0917055|bibcode=1996SJSC...17..848G |url=http://math.berkeley.edu/~mgu/MA273/Strong_RRQR.pdf|accessdate=22 September 2014}} The singular value decomposition can be used to generate an RRQR, but it is not an efficient method to do so.{{cite journal|last=Hong|first=Y.P.|author2=C.-T. Pan |title=Rank-Revealing QR Factorizations and the Singular Value Decomposition|journal=Mathematics of Computation|date=Jan 1992|volume=58|issue=197|pages=213–232|jstor=2153029|doi=10.2307/2153029|url=https://zenodo.org/record/1235097}} An RRQR implementation is available in MATLAB.{{cite web |date=29 March 2007 |title=RRQR Factorization |url=http://www.mpi-magdeburg.mpg.de/mpcsc/downloads/rrqr/Readme.pdf |url-status=dead |accessdate=2 April 2011}}