Block Algorithm and Its Implementation for Cholesky Factorization

Jianping Chen, Zhe Jin, Quan Shi, Jianlin Qiu, Weifu Liu
Block algorithm divides a large matrix into small blocks of submatrices to make full use of computer's caches. Blocked smaller submatrices can be directly loaded into the caches to compute. The efficiency of the computation is hence improved. The block algorithm for Cholesky factorization is studied in this paper. Detai1ed derivation and implementation of the block algorithm are presented. The computations of modules involved in the block algorithm are discussed. A C++ language program is
more » ... ped. It is tested and compared with the standard (unblocked) version of the Cholesky factorization. The testing results show that the presented block algorithm outperforms the unblocked one in the cases of large matrices, with an increase of execution speed of 20%.