Fast construction of hierarchical matrix representation from matrix-vector multiplication

We develop a hierarchical matrix construction algorithm using matrixvector 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.

• Type: Journal
• Year: 2011
• Where: JCPHY
• Authors: Lin Lin, Jianfeng Lu, Lexing Ying
• Keywords: Construction Algorithm, JCPHY 2011, Singular Value Decomposition, Test Vectors