Question

I am calculating the inverse of a square matrix using different libraries via Cholesky factorization. However my results are not as I was expecting. I am not an expert in maths, but I was expecting to get a closer result.

I am using MLK, magma and CULA libraries to calculate the inverse of a matrix in CPU and GPUs.
After doing the calculation those libraries I’ve noticed the results always differ in one element. Say I want to calculate the inverse of A= [0.237306,0.000458;0.000458,0.238497]:

A[0] = 0.237306 
A[1] = 0.000458 
A[2] = 0.000458 
A[3] = 0.238497

The result I obtain is:

inv(A)[0] = 4.213983 
inv(A)[1] = -0.008092 
inv(A)[2] = 0.000458 
inv(A)[3] = 4.192946 

However, the correct result should be

   4.2139841  -0.0080924
  -0.0080924   4.1929404

As you can see, inv(A)[3] is different, although the rest of them are fine. Is that how Cholesky Inversion should work? Is this a correct/approximate result or am I doing something wrong here?

Answer 1

I understand what is going on. This libraries calculate the inverse of the matrix, upper or lower as Alexandre C pointed out. So depending on the argument you pass to the library (Upper or Lower), it calculates the inverse of the upper or lower side of the matrix.
I thought you could calculate the complete inverse matrix, but apparently it is not possible this way.