Hello People!

I have a question regarding how researchers use the matrices from the sparse matrix marketplace(https://sparse.tamu.edu/) for solving linear systems of equations.

So given that we have to solve for x in : Ax = b

The matrices from the market are the A for the above equation. But what about the vector b? How do we decide on that? Do we just pre-select some random vector x and multiply A with it to give us the vector b, and use that vector b to recalculate x using some method (that's the focus of the researcher)? Or is it something else.

I've come across some papers where people mention the name of the matrices taken for testing and their initial guess vector x0. But I am confused as to how to they select a vector b? Is there a general practice? Or does it depend from author to author

There must be something I am missing, might be very silly, so I apologize in advance!

Some Papers for reference and example (with page numbers) :

Page 6-7 of:

Article Alternating Anderson-Richardson method: An efficient alterna...

Page 848 -849 of :

Article Parallel Preconditioning with Sparse Approximate Inverses

Thanks !