Algorithm 740: Fortran subroutines to compute improved incomplete Cholesky factorizations

ABSTRACT

Efficient and reliable code to compute incomplete Cholesky factors of sparse matrices for use as preconditioners in a conjugate gradient algorithm is described. This code implements two recently developed, improved incomplete factorization algorithms. An efficient implementation of the standard incomplete Cholesky factorization is also included.

REFERENCES

• 1: JONES, M. T. AND PLASSMANN, P. E. 1991. An improved incomplete Cholesky factorization. Preprint MCS-P206-0191, MCS Division, Argonne National Laboratory, Argonne, Ill.
• 2: MEIJERINK, J. AND VAN DER VORST, H.A. 1977. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-Matrix. Math. Comput. 31, 137 (Jan.), 148-162.
• 3: SEAGER, M. 1988. A SLAP for the masses. Tech. Rep. UCRL-100267, Lawrence Livermore National Laboratory.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Sparse, structured, and very large systems (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

General Terms:
Algorithms, Performance

Keywords:
incomplete Cholesky, incomplete factorization, preconditioners, sparse matrices