Basic question regarding matrix inversion vs solver

[Mads_Trolle]

Dear all,

Given a matrix A, I need to calculate element (1,1) of its inverse... i.e. if B = inv(A), i need B(1,1), and not the entire matrix B.

Hence, doing a complete inversion of matrix A seems a bit excessive... Does mkl contain any smart solver-based routines i might use...?

My first impression is to use

call getrf(A,i)
call getrs(A,I)

where I = [1,0,0,...], to get the first column of B...

Best,

Mads

[Ying_H_Intel · Accepted solution]

Hi Mads, 

You are right. If the matrix is dense, then I’d suggest to use ?gesv(A,I) as it is a bit simpler than using factorization and solve routines. If the matrix A is sparse, it is possible to use PARDISO solver with right-hand side “I” and partial solve to get just B(1,1).

Best 
Ying

[Mads_Trolle]

Dear Ying,

Thank you! Exactly what I was looking for :)

Best,

Mads