Algorithm 8 xx : a concise sparse Cholesky factorization package

The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 executable lines of code. The package is written in C, and includes a MATLAB interface.

[1]  Anoop Gupta,et al.  Efficient sparse matrix factorization on high performance workstations—exploiting the memory hierarchy , 1991, TOMS.

[2]  G. W. Stewart,et al.  Building an Old-Fashioned Sparse Solver , 2003 .

[3]  Alan George,et al.  The Design of a User Interface for a Sparse Matrix Package , 1979, TOMS.

[4]  John R. Gilbert,et al.  Sparse Matrices in MATLAB: Design and Implementation , 1992, SIAM J. Matrix Anal. Appl..

[5]  Joseph W. H. Liu,et al.  A generalized envelope method for sparse factorization by rows , 1991, TOMS.

[6]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[7]  Joseph W. H. Liu,et al.  On the storage requirement in the out-of-core multifrontal method for sparse factorization , 1986, TOMS.

[8]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[9]  Joseph W. Liu,et al.  A compact row storage scheme for Cholesky factors using elimination trees , 1986, TOMS.

[10]  J. Gilbert,et al.  Sparse Partial Pivoting in Time Proportional to Arithmetic Operations , 1986 .

[11]  Timothy A. Davis,et al.  Algorithm 837: AMD, an approximate minimum degree ordering algorithm , 2004, TOMS.

[12]  Joseph W. H. Liu The role of elimination trees in sparse factorization , 1990 .

[13]  E. Ng,et al.  An E cient Algorithm to Compute Row andColumn Counts for Sparse Cholesky Factorization , 1994 .

[14]  Alan George,et al.  Computer Solution of Large Sparse Positive Definite , 1981 .

[15]  Barry W. Peyton,et al.  A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors , 1991, SIAM J. Sci. Comput..