Lin, L; Lu, J; Ying, L, *Fast construction of hierarchical matrix representation from matrix–vector multiplication*,
Journal of Computational Physics, vol. 230 no. 10
(May, 2011),
pp. 4071-4087 [doi] .
**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(logn) applications of the matrix on structured random test vectors and O(nlogn) 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. © 2011 Elsevier Inc.*