CALCULATING THE SINGULAR VALUES AND PSEUDOINVERSE OF A MATRIX

By B. AfeArd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Polytopic Decomposition of Linear Parameter-Varying Models by Tensor-Product Model Transformation (2006, unknown): “Petres Zoltán i”
Eigenvalue statistics for beta-ensembles (2003, methodology): “The bidiagonalization method is due to Golub and Kahan [34], while the tridiagonalization method is due to Householder [40].”
Conversion of EEG activity into cursor movement by a brain-computer interface (BCI) (2004, methodology): “The parameters and 0 were obtained by the pseudoinverse method [1], [8] which minimizes the sum squared error (SSE)”
Sorting variables by using informative vectors as a strategy for feature selection in multivariate regression (2009, methodology): “Manne [24] has shown that PLS1 is equivalent to an algorithm developed by Golub and Kahan [25] for matrix bidiagonalization.”
The Optimal Hard Threshold for Singular Values is $4/\sqrt {3}$ (2014, methodology): “2323359 The default estimation technique for our task is Truncated SVD (TSVD) [2]: Write”
MIMO Transceiver Design via Majorization Theory (2007, methodology): “For comparison, reduction of H to bidiagonal form by the Golub–Kahan bidiagonalization scheme [51] (also see [52, 56, 167]), often the first step in the computation of the SVD, requires O(mnK) flops.”
Computation of the Singular Value Decomposition (2006, background): “The developments for it can be found in [GK65], [GK68], [BG69], and [GR70].”