Singular value decomposition: Difference between revisions

Revision as of 23:43, 30 January 2008

Revision as of 18:12, 2 February 2008

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In 1907, [[Erhard Schmidt]] defined an analog of singular values for [[integral operator]]s (which are compact, under some weak technical assumptions); it seems he was unaware of the parallel work on singular values of finite matrices. This theory was further developed by [[Émile Picard]] in 1910, who is the first to call the numbers <math>\sigma_k</math> ''singular values'' (or rather, ''valeurs singulières'').

Practical methods for computing the SVD date back to [[Ervand Kogbetliantz|Kogbetliantz]] in 1954, 1955 and [[Magnus Hestenes|Hestenes]] in 1958 resembling closely the [[Jacobi eigenvalue algorithm]], which uses plane rotations or [[Givens rotation]]s. However, these were unknownreplaced untilby 1965the method of when [[Gene H. Golub|Gene Golub]] and [[William Kahan]] published theirin algorithm1965 {{harv|Golub|Kahan|1965}}, which uses [[Householder transformation]]s or reflections.

In 1970, Golub and [[Christian Reinsch]] published a variant of the Golub/Kahan algorithm that is still the one most-used today.