Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

The heterogenous multiscale method (HMM) is presented as a general methodology for the
efficient numerical computation of problems with multiscales and multiphysics on multigrids …

This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods,
including the fundamental design principles behind the HMM philosophy and the main …

Although numerical approximation and statistical inference are traditionally covered as
entirely separate subjects, they are intimately connected through the common purpose of …

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/
multiresolution method for PDEs with rough (L^∞) coefficients with rigorous a priori …

The heterogeneous multi-scale method (HMM) is a general strategy for dealing with
problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies …

Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

We develop a hierarchical matrix construction algorithm using matrix–vector multiplications,
based on the randomized singular value decomposition of low-rank matrices. The algorithm …