linear system problem

linear system problem

[e70443]

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Dear sirs, 
I am a student of Computer Engineering at Madrid
University, Spain.
First of all I want to congratulate you for the
very useful "Scientific Library GSL" you have.
 
The matter that concerns me is:

I need to solve the linear system A x = b, where A
is a rectangular M-by-N matrix, and M > N. Looking the
functions of the library, I decided to use de QR descomposition. 
Before any calculation, I create the A matrix and b vector view, the 'x' 
and 'tau' vectors of N size, and the 'residual' vector of M size.
 First, I call the function gsl_linalg_QR_decomp() with the matrix A and 
the vector 'tau'. Then I call the gsl_linalg_QR_lssolve() function with 
the arguments A (with the QR descomposition created by the previous 
function), tau, b, x, and residual, to find the solution to the linear 
 system.
 I´m almost sure that these equations are correct but
 the solution is not. 
 What should I expect ? 
 My question is; am I either using the right functions, or puting them in 
the right order? 
 Shall I use another kind of descomposition?
 
   Thank you very much for your cooperation 
    
   Sincerely,
   Jaime Carsi Jaudenes.




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Re: linear system problem

[Brian Gough]

e70443@estudiante.uam.es writes:
 > I need to solve the linear system A x = b, where A is a rectangular
 > M-by-N matrix, and M > N. Looking the functions of the library, I
 > decided to use de QR descomposition.  Before any calculation, I
 > create the A matrix and b vector view, the 'x' and 'tau' vectors of
 > N size, and the 'residual' vector of M size.
 >  First, I call the function gsl_linalg_QR_decomp() with the matrix
 > A and the vector 'tau'. Then I call the gsl_linalg_QR_lssolve()
 > function with the arguments A (with the QR descomposition created
 > by the previous function), tau, b, x, and residual, to find the
 > solution to the linear
 >  system.  I´m almost sure that these equations are correct but the
 >  solution is not.  What should I expect ?  My question is; am I
 >  either using the right functions, or puting them in
 > the right order?
 >  Shall I use another kind of descomposition?

Hi,

Using the method of QR decomposition with lssolve as you describe it
should work.  See the program linalg/test.c for the lssolve example in
the test suite.

I would suggest printing out the matrices at each stage and checking
their values to see where the problem is occurring.  You can check the
results in GNU Octave, for example.

If you can find a simple case where it fails please post the code as a
bug report to bug-gsl@gnu.org.

regards

-- 
Brian Gough