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I'm working on some c++ code to solve (conjugate gradient, least squares conjugate gradient, LSQR,..) large sparse overdetermined systems of linear equations. There is a twist to my matrices and the system they're running on, that's why I code the solver myself.

For testing, debugging and benchmarking purposes I'm looking for some test matrix-vector-problems with well known solutions. I would like to be able to generate such systems for varying matrix size N x M. (Typically I deal with matrices of the size 10^7 x 10^5 with 10^9 non-zero elements.)

Do you know any such matrix-vector-systems what can easily be generated?

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I use the following website http://www.cise.ufl.edu/research/sparse/matrices/ and, in particular, this collection http://yifanhu.net/GALLERY/GRAPHS/search.html when I need to find certain kind of matrices.

Another large collection of matrices is MatrixMarket, though it is a little bit outdated in my opinion.

If you search for rectangular matrices, you would be able to find matrices you are interested in. However, there are now sample RHS's and solutions. I guess you might use an SVD-based solver to get a reference solution for your iterative solver.

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