[Lapackpp-devel] LAPACK++: Error with ill-conditioned system

[Stefano C. <ste...@an...>]

Hi,

first of all: I have been using Lapack++ over the last two years and,
well, thanks a lot for developing it. It has been of much use in my
research (I'm an OR PhD student).

I am registering an issue when solving an ill-conditioned system Ax = b,
where
A = [ 0.138071  -0.683418  0.169102 ;
-0.333333  -0.471405  0.816497 ;
1  -2.82843  0 ]

and b = [  1 1 1]'.

The solutions I get, with the three LinearSolve functions in Lapack++, are

LaLinearSolve: [1.04761e+15 3.70385e+14 6.41525e+14]
with residuals = [0.0132217 -0.00119019 -0.117126]

LaLULinearSolve: [1.04761e+15 3.70385e+14 6.41525e+14]
with residuals = [0.0132217 -0.00119019 -0.117126]

LaQRLinearSolve: [9.25854e+14 3.27339e+14 5.66968e+14]
with residuals = [-0.0255127 0.099823 0.0626831]

With GNU Octave 3.3.3. I get the solution:
  -2.6147e+06
  -9.2445e+05
  -1.6012e+06
with residuals
   1.00000
   1.00000
   1.00000

I though the underlying FORTRAN LAPACK routines used by Lapack++ and
Octave were the same, though it seems that they are not. Is it possible
that there is some issue in the linear system solving routines?

Can I give you more any more detailed information?

Thanks a lot,
-Stefano