  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.
