Root shows non singular circulant matrix to be singular and fails the FFT

Newbie
1

ROOT Version: 6.18/04
Platform: Ubuntu 19.10
Compiler:
g++ 4:9.2.1-3.1ubuntu1 amd64 GNU C++ compiler

Dear Root community,

I am currently trying to reproduce this paper DOI: 10.1137/S1064827500383123 but Root says that the matrix circ(0.5,0.25,0,…,0.25) is singular even though the determinant is >0 or for a 6x6 version of that matrix, the determinant is 33/2048~0.02. The precise error message is:
Error in TDecompLU::DecomposeLUCrout: matrix is singular
I get the same error for other circulant matrices and have cross checked with Print() that the matrices are written correctly:

     |      0    |      1    |      2    |      3    |      4    |
----------------------------------------------------------------------
   0 |        0.5        0.25           0           0           0 
   1 |       0.25         0.5        0.25           0           0 
   2 |          0        0.25         0.5        0.25           0 
   3 |          0           0        0.25         0.5        0.25 
   4 |          0           0           0        0.25         0.5 
   5 |       0.25           0           0           0        0.25 


     |      5    |
----------------------------------------------------------------------
   0 |       0.25 
   1 |          0 
   2 |          0 
   3 |          0 
   4 |       0.25 
   5 |        0.5

In a past post it was suggested to scale the matrix beforehand, but this did not solve the issue for me.
I believe this might also be the reason why the FFT solution of the linear system of equations later fails, but I am not sure.
Can you help me with this please?

Thank you

2

The determinant of this matrix is 0.

3

Oh, I used the wrong formula, thank you. With the determinant in terms of roots of unity one can rewrite the determinant as sum of cosines and then find the factor with is 0 and makes the determinant 0.
Can this topic be deleted? Sorry for the trouble