I am using Matlab to solve Ax=b and my A is very large, sparse, binary and also rectangular. I saw the Matlab backlash \ operator help and it states that if A is rectangular then it will use the QR solver to solve it. I was wondering if this is the right approach, because QR is not efficient for large sparse matrices. If this is true, then what method would you recommend to solve my system of equations?
It depends on the sparsity pattern. As a first point, did you define your matrix as a sparse matrix, because Matlab has a different suite of operations that it applies to sparse matrices, compared to sparsely filled dense matrices. Depending on your problem, you can use also iterative methods, which also have different implementations for sparse matrices. Depending on your sparsity pattern, you can also specify a smarter pre-ordering to be more efficient with the fill-ins, if you use a direct solver.