Computing the Generalized Singular Value Decomposition
Copyright policy )Computing the Generalized Singular Value Decomposition
Two new elements are added to \textit{C. C. Paige's} algorithm [SIAM J. Sci. Stat. Comput. 7, 1126-1146 (1986; Zbl 0621.65030)]. A new preprocessing step is introduced which reduces both matrices to upper triangular form satisfying certain rank conditions, and a new \(2\times 2\) triangular generalized singular value decomposition algorithm is developed for the inner loop of the algorithm. Stability analysis is given and numerical examples are presented on which all previous methods fail.
Numerical computation of eigenvalues and eigenvectors of matrices, numerical examples, Other matrix algorithms, stability, generalized singular value decomposition algorithm, matrix decomposition
Numerical computation of eigenvalues and eigenvectors of matrices, numerical examples, Other matrix algorithms, stability, generalized singular value decomposition algorithm, matrix decomposition
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).69 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!