We consider the eficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix being stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code, but substantially outperforms it. Furthermore, it compares favourably to using conventional full format (LAPACK) and using the recursive format of Andersen, Gustavson, and Wasniewski.
novel packed matrix data structures; linear systems of equations; Cholesky factorization and solution; real symmetric matrices; complex Hermitian matrices; recursive algorithms; positive definite matrices