Editing QR algorithm (section)

== Other variants ==
One variant of the ''QR algorithm'', ''the Golub-Kahan-Reinsch'' algorithm starts with reducing a general matrix into a bidiagonal one.<ref>Bochkanov Sergey Anatolyevich. ALGLIB User Guide - General Matrix operations - Singular value decomposition . ALGLIB Project. 2010-12-11. URL:[http://www.alglib.net/matrixops/general/svd.php] Accessed: 2010-12-11. (Archived by WebCite at https://www.webcitation.org/5utO4iSnR?url=http://www.alglib.net/matrixops/general/svd.php</ref> This variant of the ''QR algorithm'' for the computation of [[singular values]] was first described by {{harvtxt|Golub|Kahan|1965}}. The [[LAPACK]] subroutine [http://www.netlib.org/lapack/double/dbdsqr.f DBDSQR] implements this [[iterative method]], with some modifications to cover the case where the singular values are very small {{harv|Demmel|Kahan|1990}}. Together with a first step using Householder reflections and, if appropriate, [[QR decomposition]], this forms the [http://www.netlib.org/lapack/double/dgesvd.f  DGESVD] routine for the computation of the [[singular value decomposition]]. The QR algorithm can also be implemented in infinite dimensions with corresponding convergence results.<ref>{{cite journal |first1=Percy |last1=Deift |first2=Luenchau C. |last2=Li |first3=Carlos |last3=Tomei|title=Toda flows with infinitely many variables |journal=Journal of Functional Analysis |volume=64 | number=3| pages=358–402 |year=1985 |doi=10.1016/0022-1236(85)90065-5|doi-access=free }}</ref><ref>{{cite journal |first1=Matthew J. |last1=Colbrook |first2=Anders C.|last2=Hansen|title=On the infinite-dimensional QR algorithm |journal=Numerische Mathematik |volume=143 | number=1| pages=17–83 |year=2019 |doi=10.1007/s00211-019-01047-5|arxiv=2011.08172|doi-access=free }}</ref>