SVD - Singular Value Decomposition 14-FEB-2017

[Werner]

(10-21-2015 06:20 PM)Werner Wrote:  The 48/49 use the older LINPACK version (but without the shift calculation bug) that does not have the zero-shift QR nor bulge chasing in two directions, and different (simpler - too simple in some cases) convergence criteria.

Well there goes my memory.
The 48/49/50 use the LAPACK version, as well.
How can you know?
1. look at the source code, or:
2. calculate the SVD of

Code:


  [ a^2 1  0  0  ]
  [  0  1  a  0  ]
  [  0  0  1  1  ]
  [  0  0  0 a^2 ]

with a very small a so that 1+a = 1. (I used a=10^-20)
When the smallest singular value is about a^3, the LAPACK code is used.
When it's a^2/SQRT(2), the LINPACK code is used.
(the LINPACK code would set the offdiagonal a to zero since the convergence test used is 1 + 1 + a = 1 + 1 (adding the neighbouring diagonal elements)

Cheers, Werner