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A note on the error analysis of classical Gram-Schmidt | | Alicja Smoktunowicz
; Jesse L. Barlow
; Julien Langou
; | | Date: |
11 Jun 2006 | | Subject: | Numerical Analysis | | Abstract: | An error analysis result is given for classical Gram--Schmidt factorization of a full rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular. The work presented here shows that the computed $R$ satisfies $
ormal{R}=
ormal{A}+E$ where $E$ is an appropriately small backward error, but only if the diagonals of $R$ are computed in a manner similar to Cholesky factorization of the normal equations matrix.
A similar result is stated in [Giraud at al, Numer. Math. 101(1):87--100,2005]. However, for that result to hold, the diagonals of $R$ must be computed in the manner recommended in this work. | | Source: | arXiv, math/0606258 | | Services: | Forum | Review | PDF | Favorites | |
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