Author:
Reinsch Christian,Richter Mathias
Abstract
AbstractA well-known and successful algorithm to compute the singular value decomposition (SVD) of a matrix was published by Golub and Reinsch (Numer. Math. 14:403–420, 1970), together with an implementation in Algol. We give an updated implementation in extended double precision arithmetic in the C programming language. Extended double precision is native for Intel x86 processors and provides improved accuracy at full hardware speed. The complete program for computing the SVD is listed. Additionally, a comprehensive explanation of the original algorithm of Golub and Reinsch (Numer. Math. 14:403–420, 1970) is given at an elementary level without referring to the more general results of Francis (Comput. J. 4:265–271, 1961, 1962).
Funder
Universität der Bundeswehr München
Publisher
Springer Science and Business Media LLC
Reference5 articles.
1. Francis, J.: The QR transformation. A unitary analogue to the LR transformation. Comput. J. 4, 265–271 (1961, 1962)
2. Gander, W.: The first algorithms to compute the SVD, https://people.inf.ethz.ch/gander/talks/Vortrag2022.pdf
3. Golub, G.H., Reinsch, C.: Singular value decomposition and least squares solutions. Numer. Math. 14, 403–420 (1970)
4. Higham, N.J.: Acuracy and Stability of Numerical Algorithms, 2nd edn. SIAM (2002)
5. Wilkinson, J.H.: Global convergence of tridiagonal QR algorithm with origin shifts, Lin. Alg. Appl., 409–420 (1968)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献