SC²S Colloquium - November 10, 2011

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Date: November 10, 2011
Room: 02.07.023
Time: 15:00 am, s.t.

Jürgen Bräckle: A Block Version of the Factorized Sparse Approximate Inverse Preconditioner (FSPAI)

The talk is concerned with the factorized sparse approximate inverse (FSPAI) preconditioning technique for symmetric positive definite (SPD) systems Ax = b. FSPAI is inherently parallel and finds a lower triangular matrix L for the split preconditioned system L^T A L y = L^T b and Ly = x. No a priori knowledge on the sparsity pattern for L is necessary as the algorithm automatically captures most profitable indices to improve on a current approximation. A detailed analysis of the FSPAI provides theoretical properties and makes it possible to derive an exact version of the FSPAI (EFSPAI). The EFSPAI updates its sparsity pattern by optimal indices. In the second part of the talk, we derive the theory for the block version of FSPAI (BFSPAI) which allows efficient preconditioning of block SPD systems.