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      Fast construction of hierarchical matrix representation from matrix-vector multiplication

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          Abstract

          We develop a hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses \(\mathcal{O}(\log n)\) applications of the matrix on structured random test vectors and \(\mathcal{O}(n \log n)\) extra computational cost, where \(n\) is the dimension of the unknown matrix. Numerical examples on constructing Green's functions for elliptic operators in two dimensions show efficiency and accuracy of the proposed algorithm.

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          A fast algorithm for particle simulations

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            Fast wavelet transforms and numerical algorithms I

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              Nested Dissection of a Regular Finite Element Mesh

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                Author and article information

                Journal
                31 December 2009
                2010-08-20
                Article
                1001.0149
                96157d61-73df-48e3-999a-6713fede1e07

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                65F30 (Primary), 65C20 (Secondary)
                math.NA

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