Abstract
In September 1991 J. W. Demmel and W. M. Kahan were awarded the second SIAM prize in numerical linear algebra for their paper ‘Accurate Singular Values of Bidiagonal Matrices’ [1], referred to as DK hereafter. Among several valuable results was the observation that the standard bidiagonal QR algorithm used in LINPACK [2], and in many other SVD programs, can be simplified when the shift is zero and, of greater importance, no subtractions occur. The last feature permits very small singular values to be found with (almost) all the accuracy permitted by the data and at no extra cost.
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References
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© 1993 Springer Science+Business Media Dordrecht
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Fernando, K.V., Parlett, B.N. (1993). Accurate Singular Values and Differential QD Algorithms. In: Moonen, M.S., Golub, G.H., De Moor, B.L.R. (eds) Linear Algebra for Large Scale and Real-Time Applications. NATO ASI Series, vol 232. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8196-7_32
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DOI: https://doi.org/10.1007/978-94-015-8196-7_32
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