Iterative solution methods based on the Hierarchically Semi-Separable Representation
نویسندگان
چکیده
In this paper, we study an important class of structured matrices: ”Hierarchically Semi-Separable (HSS)” matrices, for which an efficient hierarchical state based representation called Hierarchically Semi-Separable (HSS) representation can be used to utilize the data sparsity of the HSS matrices. A novel algorithm with O(n) complexity is proposed to construct suboptimal HSS representations from sparse matrices. Subsequently, the limitation of the direct HSS solution method is discussed in this paper, and a general strategy to combine standard iterative solution methods with the HSS representation is presented. We also describe a number of preconditioner construction algorithms based on the HSS representation. Our numerical experiments indicate that these iterative solution methods have linear complexity in computation time.
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