Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses
Copyright policy )Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses
Sparse approximate inverses (SPAI) are matrices \(M=(m_1 , m_2, \ldots , m_n)\) with a given sparsity pattern such that \(|e_k - A m_k|\) is minimal for each \(k\). Explicitly known smoothers (or preconditioners) have the advantage that they are suitable for parallel computers in contrast to Gauss-Seidel or ILU. It is shown that SPAI(0), i.e. diagonal matrices of this type are better than damped Jacobi although there is no parameter in SPAI(0). There are also some results for lesss sparse cases.
Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Numerical computation of matrix norms, conditioning, scaling, Parallel numerical computation, Gauss-Seidel method, comparison of methods, smoothers, incomplete LU-factorization, preconditioners, Computational methods for sparse matrices, smoothing property, parallel computation, multigrid, sparse approximate inverses, damped Jacobi method
Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Numerical computation of matrix norms, conditioning, scaling, Parallel numerical computation, Gauss-Seidel method, comparison of methods, smoothers, incomplete LU-factorization, preconditioners, Computational methods for sparse matrices, smoothing property, parallel computation, multigrid, sparse approximate inverses, damped Jacobi method
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