The design and implementation of a new out-of-core sparse Cholesky factorization method

We describe a new out-of-core sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtree-scheduling algorithm, and both right-looking and left-looking updates. The implementation of the new method is efficient and robust. On a 2 GHz personal computer with 768 MB of main memory, the code can easily factor matrices with factors of up to 48 GB, usually at rates above 1 Gflop/s. For example, the code can factor AUDIKW, currenly the largest matrix in any matrix collection ( factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-140 mesh in about 12 hours ( factor size around 27 GB).