[Octave-bug-tracker] [bug #55727] Feature request: add GEJSV as an additional svd_drivers

[count]

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

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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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