CHOLMOD is very fast, but I am just wondering what kinds of size A such that it can solve Ax=b. I have a A of 200,000 * 200,000, but it outputs errors" problem too large". I am very appreciated if anyone can tell me which solver/software for numerical computing can solve such large size problem. Thanks!
The storage required by a sparse matrix depends (roughly linearly) on the number of nonzero elements in the matrix. When you then attempt to compute a Cholesky factorization (or more generally an LU factorization) of your sparse matrix, the factors typically have substantially more nonzero elements than the original matrix had- this is referred to as "fill-in."
The amount of fill-in that occurs will depend on the number and placement of the nonzeros in the original matrix. In many cases you can reduce fill-in by carefully ordering the rows/columns of your matrix before factoring it. There are many algorithms for reducing the fill-in, but computing an optimal ordering is an NP-hard problem, so in practice these algorithms use heuristic approaches to get a good fill-in reducing ordering.
It appears that CHOLMOD couldn't factor your matrix because there wasn't sufficient storage available to handle the fill-in that occurred during the factorization process. Did you reorder the rows/columns of your matrix before factoring it to reduce fill-in? If not, then using a good ordering might be enough to make this problem solvable within the memory that you have available.
Can you try to solve your problem on a computer with more memory?