Fast construction of hierarchical matrix representation from matrix-vector multiplication
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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.
Published Version (Please cite this version)10.1016/j.jcp.2011.02.033
Publication InfoLin, L; Lu, Jianfeng; & Ying, L (2011). Fast construction of hierarchical matrix representation from matrix-vector multiplication. Journal of Computational Physics, 230(10). pp. 4071-4087. 10.1016/j.jcp.2011.02.033. Retrieved from https://hdl.handle.net/10161/14064.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.