I don't see how you concluded that the two have the same functionality. There is some overlap, perhaps, but note this: Pardiso is applicable only to square matrices. The Q-R decomposition is obtained for various purposes, one of which is obtaining a least squares solution of over-determined linear equations.
If you have a class of matrices for which both are applicable, and the matrices are well-conditioned, I would expect Pardiso to be more efficient, but you would have to try both and judge for yourself.
Sorry, I have seen that in MKL documentation.
I understand that SparseQR is used to factorize sparse matrices and can also be used to solve a sparse linear system of equations. At least, the title Sparse QR is:
"The Sparse QR routines provide a multifrontal sparse QR factorization method for solving a sparse system of linear equations.'
I am using PARDISO to solve a sparse linear of equations, and at least it is what I understand PARDISO is for.
Even if the 2 functions can do other things, at least they can both be used to solve a linear system with a sparse matrix. To me, this is the same functionality and it is an important one, at least for me. My question was justified. I understand PARDISO is faster.
Thanks for your nice answer.
You may find some benchmark results at https://software.intel.com/en-us/articles/intel-sparse-qr-factorization-prototype-preview-package . Note, however, that the article is about a preview version of Intel Sparse QR, so the timings may not be valid for the current release.
As far as I can see, the test matrices in the benchmark (you can see the names of the matrices on the graph) have more rows than columns, and details of these matrices are available at https://sparse.tamu.edu/.
I am not aware of any comparisons to Pardiso in the context of square matrices, but let us hope that someone from Intel may be able to comment on that question.