I am currently looking at a problem which involves the solution of min||Ax-b||, where A is a very large dense complex matrix, and b is a complex vector. Here very large means matrix size of 10000*10000 at least.

I searched documentation for cuSolver, but it seems that cuSolver cannot solve this issue, because its dense solver assumes A to be a square matrix. While its sparse solver supports non-square problem, it does not apply to my issue because my matrix A is a dense matrix.

I wonder if anyone in this forum has solved a similar problem before. Thank you!

The MAGMA library supports solving least-squares problems with dense matrices. See http://icl.cs.utk.edu/projectsfiles/magma/doxygen/group__magma__gels.html . Each matrix in your case will occupy at least 1 GB memory, so you might need a GPU with as much memory as possible. What kind of engineering problems gives such large dense matrices ?

It is a numerical acoustics problem. Actually I am using boundary element method to solve it. However, for high frequency components, the data set is extremely large.

The reason why I choose gpu is because I have to calculate each element in matrix A, so generating A itself would take me too much time. With A completed, the least square problem I mentioned above will need to be solved.