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Equal spaced singular values in (0, 1] the largest singular values, and the corresponding vectors, is needed [11,22, 23,28,29]. Once the upper triangular semiseparable matrix has been transformed to unreducible form, its singular values can be computed reapplying A QR–method for computing the singular values via semiseparable matrices 193 Comparison in accuracy for singular values 1:n −13 10 maximum relative error of the eigenvalues Semi Separable QR Traditional QR −14 10 −15 10 −16 10 50 100 150 200 250 300 Size of the matrices 350 400 450 500 Fig.

SIAM J. Matrix Anal. Appl. 12(2), 374–384 (1991) A QR–method for computing the singular values via semiseparable matrices 195 27. : Theory of decomposition and bulge-chasing algorithms for the generalized eigenvalue problem. SIAM J. Matrix Anal. Appl. 15(3), 943–967 (1994) 28. : Principal component analysis for clustering gene expression data. Bioinformatics. 17(9), 763–774 (2001) 29. : Reverse engineering gene networks using singular value decomposition and robust regression. In Proceedings of the national academy of sciences of the united states of america.

Appl. Math. 164–165, 731–747 (2004) 20. : An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices. Leuven, Leuven, Belgium, August 2003 21. : A note on the representation and definition of semiseparable matrices. Numerical Linear Algebra with Applications. May 2004. Accepted for publication (Report TW393) 22. : Svdman - singular value decomposition analysis of microarray data. Bioinformatics. 17(6), 566–568 (2001) 23. : Singular value decomposition and principal component analysis.

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