A compact row storage scheme for Cholesky factors using elimination trees

Abstract

For a given sparse symmetric positive definite matrix, a compact row-oriented storage scheme for its Cholesky factor is introduced. The scheme is based on the structure of an elimination tree defined for the given matrix. This new storage scheme has the distinct advantage of having the amount of overhead storage required for indexing always bounded by the number of nonzeros in the original matrix. The structural representation may be viewed as storing the minimal structure of the given matrix that will preserve the symbolic Cholesky factor. Experimental results on practical problems indicate that the amount of savings in overhead storage can be substantial when compared with Sherman's compressed column storage scheme.