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Fix xORBDB6 performs numerically unadvisable operations #647

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Merged
merged 10 commits into from
Jul 15, 2022
Merged

Fix xORBDB6 performs numerically unadvisable operations #647

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d245b4f
SORCSD2BY1: remove dead code
christoph-conrads Oct 25, 2021
bdcd890
SORCSD: fix documentation on matrix dimensions
christoph-conrads Oct 25, 2021
643e7e3
SORBDB6: fix indexing, set vectors to zero
christoph-conrads Oct 26, 2021
774e5a9
SORBDB6: document algorithm, when output is zero
christoph-conrads Oct 26, 2021
deed8f3
SORBDB6: improve numerical stability
christoph-conrads Nov 11, 2021
a015b21
SORBDB6: replace integer literal with constant
christoph-conrads May 29, 2022
94419e8
DORBDB6: improve numerical stability, documentation
christoph-conrads Nov 11, 2021
6479e0f
CUNBDB6: improve numerical stability, documentation
christoph-conrads Nov 11, 2021
54b3964
ZUNBDB6: improve numerical stability, documentation
christoph-conrads Nov 11, 2021
145b1c3
xORBDB6/xUNBDB6: fix read of uninitialized variable
christoph-conrads Jul 14, 2022
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SORBDB6: document algorithm, when output is zero
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christoph-conrads committed Jul 10, 2022
commit 774e5a9f7b15685d575054412c230a5e995e74bc
12 changes: 8 additions & 4 deletions SRC/sorbdb6.f
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Expand Up @@ -41,10 +41,15 @@
*> with respect to the columns of
*> Q = [ Q1 ] .
*> [ Q2 ]
*> The columns of Q must be orthonormal.
*> The columns of Q must be orthonormal. The orthogonalized vector will
*> be zero if and only if it lies entirely in the range of Q.
*>
*> If the projection is zero according to Kahan's "twice is enough"
*> criterion, then the zero vector is returned.
*> The projection is computed with at most two iterations of the
*> classical Gram-Schmidt algorithm, see
*> * L. Giraud, J. Langou, M. Rozložník. "On the round-off error
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@langou langou Apr 12, 2022

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Thanks for quoting this paper.

I think the following paper is a better quote for this fact:

L. Giraud, J. Langou, M. Rozložník, Jasper van den Eshof. "Rounding error analysis of the classical Gram-Schmidt orthogonalization process." Numerische Mathematik, volume volume 101, pages 87–100, 2005. DOI = 10.1007/s00211-005-0615-4.

*> analysis of the Gram-Schmidt algorithm with reorthogonalization."
*> 2002. CERFACS Technical Report No. TR/PA/02/33. URL:
*> https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
*>
*>\endverbatim
*
Expand Down Expand Up @@ -320,4 +325,3 @@ SUBROUTINE SORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
* End of SORBDB6
*
END