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[Octave-bug-tracker] [bug #55727] Feature request: add GEJSV as an addit
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[Octave-bug-tracker] [bug #55727] Feature request: add GEJSV as an additional svd_drivers |
Date: |
Sat, 16 Feb 2019 17:24:24 -0500 (EST) |
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URL:
<https://savannah.gnu.org/bugs/?55727>
Summary: Feature request: add GEJSV as an additional
svd_drivers
Project: GNU Octave
Submitted by: count
Submitted on: Sat 16 Feb 2019 10:24:23 PM UTC
Category: Octave Function
Severity: 3 - Normal
Priority: 5 - Normal
Item Group: Feature Request
Status: None
Assigned to: None
Originator Name:
Originator Email:
Open/Closed: Open
Discussion Lock: Any
Release: dev
Operating System: Any
_______________________________________________________
Details:
Currently Octave supports two svd_drivers: GESVD and GESDD.
However, in some extreme cases, both of then are not satisfactory in terms of
relative accuracy.
Such extreme cases can occur in research. e.g. several examples in bug #55564,
e.g. total least square method needs the singular vector corresponding to the
smallest singular value. See ref1 below for more.
The Jacobi method is known to be more accurate than both QR (GESVD) and
Divide&Conquer (GESDD) method, see [ref1]. LAPACK includes such
implementations named GEJSV and GESVJ. Accuracy and speed performance is
analyzed in [ref2].
The GESVJ, is seems an internal routine for GEJSV, probably not intended for
general use.
I'm writing a patch to make GEJSV available in Octave, hope that works.
[ref1]: Jacobi’s Method is More Accurate than QR
<https://epubs.siam.org/doi/10.1137/0613074>
[ref2]: The Singular Value Decomposition: Anatomy of Optimizing an Algorithm
for Extreme Scale <https://epubs.siam.org/doi/10.1137/17M1117732>
LAPACK manual GEJSV
<http://www.netlib.org/lapack/explore-html/d1/d7e/group__double_g_esing_ga8767bfcf983f8dc6ef2842029ab25599.html#ga8767bfcf983f8dc6ef2842029ab25599>
LAPACK manual GESVJ
<http://www.netlib.org/lapack/explore-html/dd/d9a/group__double_g_ecomputational_gac14340a964d1df1b2f4483844a7c0df1.html#gac14340a964d1df1b2f4483844a7c0df1>
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