Algorithm 358: singular value decomposition of a complex matrix [F1, 4, 5]
Communications of the ACMPublished 1 October 1969Open access
Peter A. Businger, Gene H. Golub
Citations142
SJR quartileQ1
SJR score1.15
SNIP3.34
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TL;DR
The main idea is to in ter leave composit ions of x and n -x objects and resor t to a lexicographic genera t ion ofComposit ions.
Abstract
procedure Ising (n, x, t, S); integer n, x, l; integer array S; comment Ising generates n-sequences ($1, "", S,) of zeros and ones where x = ~i~ S~ and t = ~,-~1 I S~+I -S~ I are given. The main idea is to interleave compositions of x and n --x objects and resort to a lexicographic generation of compositions. We call these sequences Ising configurations since we believe they first appeared in the study of the so-called Ising
Keywords
Computer ScienceEngineeringPhysics and Astronomy
Journal of the Society for Industrial and Applied Mathematics Series B Numerical AnalysisCalculating the Singular Values and Pseudo-Inverse of a Matrix
1,773 Citations1965Gene H. Golub, W. Kahan
The use of the pseudo-inverse $A^I = V\Sigma ^I U^* $ to solve least squares problems in a way which dampens spurious oscillation and cancellation is mentioned.