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| | 计算奇异值分解的实用方法可追溯到1954-1955年 Kogbetliantz 和1958年 Hestenes 的工作<ref>{{cite journal |last1=Hestenes |first1=M. R. |title=Inversion of Matrices by Biorthogonalization and Related Results |journal=Journal of the Society for Industrial and Applied Mathematics |volume=6 |issue=1 |pages=51–90 |year=1958 |doi=10.1137/0106005 |jstor=2098862 |mr=0092215 }}</ref>。这些方法与使用平面旋转或 Givens 旋转的 Jacobi 特征值算法极为相似。然而，1965年 Gene Golub 和 William Kahan 发表的方法<ref>(Golub & Kahan 1965)</ref>取代了之前的方法，他们采用了 Householder 变换或反射。1970年，Golub 和 Christian Reinsch<ref>{{cite journal |last1=Golub |first1=G. H. |last2=Reinsch |first2=C. |title=Singular value decomposition and least squares solutions |journal=Numerische Mathematik |volume=14 |issue=5 |pages=403–420 |year=1970 |doi=10.1007/BF02163027 |mr=1553974 |s2cid=123532178 }}</ref> 发表了 Golub/Kahan 算法的一个变体，这个变体至今仍广泛应用。 | | 计算奇异值分解的实用方法可追溯到1954-1955年 Kogbetliantz 和1958年 Hestenes 的工作<ref>{{cite journal |last1=Hestenes |first1=M. R. |title=Inversion of Matrices by Biorthogonalization and Related Results |journal=Journal of the Society for Industrial and Applied Mathematics |volume=6 |issue=1 |pages=51–90 |year=1958 |doi=10.1137/0106005 |jstor=2098862 |mr=0092215 }}</ref>。这些方法与使用平面旋转或 Givens 旋转的 Jacobi 特征值算法极为相似。然而，1965年 Gene Golub 和 William Kahan 发表的方法<ref>(Golub & Kahan 1965)</ref>取代了之前的方法，他们采用了 Householder 变换或反射。1970年，Golub 和 Christian Reinsch<ref>{{cite journal |last1=Golub |first1=G. H. |last2=Reinsch |first2=C. |title=Singular value decomposition and least squares solutions |journal=Numerische Mathematik |volume=14 |issue=5 |pages=403–420 |year=1970 |doi=10.1007/BF02163027 |mr=1553974 |s2cid=123532178 }}</ref> 发表了 Golub/Kahan 算法的一个变体，这个变体至今仍广泛应用。 |
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| | ==注释== | | ==注释== |