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 decomposition|QR factorization]] which can be used to determine the [[rank (linear algebra)|rank]] of a matrix.<ref name=GuSciComput1996>{{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}}</ref> The [[singular value decomposition]] can be used to generate an RRQR, but it is not an efficient method to do so.<ref name=HongPan92>{{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}}</ref> An RRQR implementation is available in MATLAB.<ref name="RRQR Factorization MATLAB Docs">{{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 |archive-date=14 May 2011 |archive-url=https://web.archive.org/web/20110514093259/http://www.mpi-magdeburg.mpg.de/mpcsc/downloads/rrqr/Readme.pdf }}</ref>

== References == {{Reflist}}

[[Category:Matrix decompositions]] [[Category:Numerical linear algebra]]