Web28 de jul. de 2003 · In previous papers hierarchical matrices were introduced which are data-sparse and allow an approximate matrix arithmetic of nearly optimal complexity. In this paper we analyse the complexity (storage, addition, multiplication and inversion) of the hierarchical matrix arithmetics. Two criteria, the sparsity and idempotency, are … WebHierarchical matrices. The H-matrix format and its arithmetic were introduced in [19]. They are an important tool in the solution of BEM systems. An H-matrix is a dense matrix that is nevertheless data-sparse, owing to the fact that it contains many large low-rank subblocks, corresponding to pair of so-called admissible clusters.
A new fast direct solver for the boundary element method
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arXiv:2012.14287v2 [math.NA] 23 Sep 2024
Web30 de out. de 2024 · Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space complexity of dense matrix vector multiplication, and hence has been applied to … WebFast construction of hierarchical matrix representation from matrix–vector multiplication Lin Lina,⇑, Jianfeng Lub, Lexing Yingc a Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States bDepartment of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 … Web1 de jan. de 2003 · Hierarchical matrices (H-matrices) [1], [2], [3] are used as approximation techniques. An H-matrix is constructed directly from the interactions … phoenixx international pittsburgh