High performance Cholesky and symmetric indefinite factorizations with applications

摘要: The process of factorizing a symmetric matrix using the Cholesky (LL ) or indefinite (LDL factorization A allows efficient solution systems Ax = b when is symmetric. This thesis describes development new serial and parallel techniques for this problem demonstrates them in setting interior point methods. In serial, effects various scalings are reported, fast robust mixed precision sparse solver developed. parallel, DAG-driven dense factorizations developed positive definite case. These achieve performance comparable with other world-leading implementations novel algorithm same family as those given by Buttari et al. problem. Performance these context an method assessed.