Fast construction of hierarchical matrix representation from matrix-vector multiplication

2009/12/31 by Lin, Lin, Lu, Jianfeng, Ying, Lexing · 3 citations
#65C20 (Secondary) #65F30 (Primary) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1001.0149

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 O(log n) applications of the matrix on structured random test vectors and 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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