Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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A new class of approximate inverse preconditioners is presented for solving large linear systems with an iterative method. It is at the intersection of multipole, multigrid and SPAI methods. The method consists in approximating the inverse of a matrix by a block constant matrix, instead of approximating it by a sparse matrix as in SPAI methods. It does not require more storage, or even less, and it is well suited for parallelization, both for the construction of the preconditioner and for the matrix-vector product at each iteration.