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math.NA2016★ 1 cited
A sparse decomposition of low rank symmetric positive semi-definite matrices
Thomas Y. Hou, Qin Li, Pengchuan Zhang
Suppose that is symmetric positive semidefinite with rank . Our goal is to decompose into rank-one matrices $\sum_{k=1}^K g_k g_k^T…
math.NA2016★ 1 cited
Exploring the locally low dimensional structure in solving random elliptic PDEs
Thomas Y. Hou, Qin Li, Pengchuan Zhang
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to sim…