Multigrid methods are one of the most efficient techniques for solving large sparse linear
systems arising from partial differential equations (PDEs) and graph Laplacians from …

Kernel methods are used frequently in various applications of machine learning. For large-
scale high dimensional applications, the success of kernel methods hinges on the ability to …

Nonlinear monotone transformations are used extensively in normalizing flows to construct
invertible triangular mappings from simple distributions to complex ones. In existing …

Hierarchical matrices provide a powerful representation for significantly reducing the
computational complexity associated with dense kernel matrices. For example, the fast …

Hierarchical matrices are scalable matrix representations particularly suited to the case
where the matrix entries are defined by a smooth kernel function evaluated between pairs of …

The spectrum of a kernel matrix significantly depends on the parameter values of the kernel
function used to define the kernel matrix. This makes it challenging to design a …

In the construction of rank-structured matrix representations of dense kernel matrices, a
heuristic compression method, called the proxy point method, has been used in practice to …

A general, rectangular kernel matrix may be defined as K ij= κ (xi, yj) K _ ij= κ\left (x _i, y
_j\right) where κ (x, y) κ\left (x, y\right) is a kernel function and where X= xi i= 1 m X=\left {x …

Generating quasirandom points with high uniformity is a fundamental task in many fields.
Existing number-theoretic approaches produce evenly distributed points in [0, 1] d in …

A novel framework for hierarchical low‐rank matrices is proposed that combines an adaptive
hierarchical partitioning of the matrix with low‐rank approximation. One typical application is …