topic Hi Mads, in Intel® oneAPI Math Kernel Library
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101762#M23939
<P>Hi Mads, </P>
<P>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).</P>
<P>Best <BR />
Ying</P>Wed, 27 Jan 2016 04:04:52 GMTYing_H_Intel2016-01-27T04:04:52ZBasic question regarding matrix inversion vs solver
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101761#M23938
<P>Dear all,</P>
<P>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.</P>
<P>Hence, doing a complete inversion of matrix A seems a bit excessive... Does mkl contain any smart solver-based routines i might use...?</P>
<P>My first impression is to use</P>
<P>call getrf(A,i)<BR />
call getrs(A,I)</P>
<P>where I = [1,0,0,...], to get the first column of B...</P>
<P>Best,</P>
<P>Mads</P>
<P> </P>
<P> </P>
<P> </P>Mon, 25 Jan 2016 09:56:46 GMThttps://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101761#M23938Mads_Trolle2016-01-25T09:56:46ZHi Mads,
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101762#M23939
<P>Hi Mads, </P>
<P>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).</P>
<P>Best <BR />
Ying</P>Wed, 27 Jan 2016 04:04:52 GMThttps://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101762#M23939Ying_H_Intel2016-01-27T04:04:52ZDear Ying,
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101763#M23940
<P>Dear Ying,</P>
<P>Thank you! Exactly what I was looking for :)</P>
<P>Best,</P>
<P>Mads</P>Fri, 29 Jan 2016 10:03:54 GMThttps://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Basic-question-regarding-matrix-inversion-vs-solver/m-p/1101763#M23940Mads_Trolle2016-01-29T10:03:54Z