Fast construction of hierarchical matrix representation from matrix-vector multiplication
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2011-05-10
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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.
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Lin, L, J Lu and L Ying (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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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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