Regarding your second test-case for the problem A x = b: Your r.h.s. vector b is zero. Unless A is singular, the solution is x = 0. Therefore, this is not much of a test.

In effect, then, you have only verified that the 5 X 5 test-case worked correctly. You may consider creating some medium-size test cases with b not equal to zero.

For the problem described by your files ia_1.txt, ja_1.txt,a_1.txt,b_1.txt the MKL DSS solver estimates the determinant to be about -10^-1204. This means that your matrix may be almost singular; if you agree with this surmise, you need to investigate the impact of this finding on your work. If you do not find it reasonable for the matrix to be nearly singular, you will have to probe into possible errors in the matrix coefficients.

I suggest that you post a few smaller examples with, say, 50,100 and 200 unknowns.

Mecej4,
The determinant of matrix A=10^{-1}*(identity matrix) with size of 10000x10000 is equal to 10^{-10000} but it doesn't singular and can't be solved by any direct method without any problem.
Daniel,
Thanks for reproducer, I will check it
With best regards,
Alexander Kalinkin

Quote:

Alexander Kalinkin (Intel) wrote:

Mecej4,
The determinant of matrix A=10^{-1}*(identity matrix) with size of 10000x10000 is equal to 10^{-10000} but it doesn't singular and can't be solved by any direct method without any problem.

Alexander, I agree that the mere fact that the determinant is small need not let one conclude that the matrix is singular.

However, the estimate of the condition number of the matrix in the case under question is (from Matlab) 7 x 10³⁵, from which one may suspect that the matrix is likely to cause problems.