Incomplete inverse triangular factorization in parallel algorithms of preconditioned conjugate gradient methods
Abstract:
A preconditioner for large sparse symmetric positive definite coefficient matrix is considered based on its approximate inverse in the form of product of a lower triangular sparse matrix by its transpose. A parallel algorithm for the construction and application of the preconditioner is proposed. A new approximate block Jacobi preconditioning method is proposed based on the use of the incomplete inverse triangular factorization of diagonal blocks. Timing results are presented for a model problem and test problems with matrices from the collection of the university of Florida for the proposed preconditioning in comparison with the 2nd order Block Incomplene Inverse Cholesky and the standard point Jacobi preconditionings.
Keywords:
iterative solution of linear systems, sparse matrices, incomplete inverse triangular factorization, parallel preconditioning, conjugate gradient method
