Fast construction of hierarchical matrix representation from matrix-vector multiplication

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 OðlognÞ applications of the matrix on structured random test vectors and Oðn lognÞ 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. All rights reserved.