topic Re: Iterative methods for sparse least square problem in Intel® oneAPI Math Kernel Library

Iterative methods for sparse least square problem

heiga — Mon, 23 Feb 2009 22:03:12 GMT

Does Intel have any plan to include iterative methods for the sparse least square problem such as LSQR, SYMMLQ, and MINRES into MKL? (or PARADISO has already included these functions?)

Re: Iterative methods for sparse least square problem

Sergey_K_Intel1 — Thu, 26 Feb 2009 09:51:49 GMT

MKL doesn't have any plan to include iterative methods for the sparse least square problems. PARDISO doesn't have such functioanality as well.

But you could try the following way. It can work if your matrix has full rank.It is known thatthe least square problem for A*x = fis equivalent to finding the solution of the system(A^T * A) x = A^T *f. MKL Sparse BLAS provides routines for computing product of two sparse matrices stored in the compressed sparse row format. The result matrix can be stored as a dense matrix orcompressed sparse row matrix. The vector A^T*f can be computed with the help of MKL sparse BLAS as well. After that PARDISO or LAPACK solver can be used for finding the solution(A^T * A) x = A^T *f.

All the best
Sergey

Re: Iterative methods for sparse least square problem

heiga — Thu, 26 Feb 2009 10:53:20 GMT

Quoting - Sergey Kuznetsov (Intel)

But you could try the following way. It can work if your matrix has full rank.It is known thatthe least square problem for A*x = fis equivalent to finding the solution of the system(A^T * A) x = A^T *f. MKL Sparse BLAS provides routines for computing product of two sparse matrices stored in the compressed sparse row format. The result matrix can be stored as a dense matrix orcompressed sparse row matrix. The vector A^T*f can be computed with the help of MKL sparse BLAS as well. After that PARDISO or LAPACK solver can be used for finding the solution(A^T * A) x = A^T *f.

Thank you very much for your reply. Unfortunately, my problem doesn't have full rank. So I'm currently using open-source version of MINRES.