相关论文: Approximation of integral operators by Green quadr…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…

Accurate computation of the Green's function is crucial for connecting experimental observations to the underlying quantum states. A major challenge in evaluating the Green's function in the time domain lies in the efficient simulation of…

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace…

We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…

This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for…

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…

In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…

We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…

We introduce a fast algorithm for entry-wise evaluation of the Gauss-Newton Hessian (GNH) matrix for the fully-connected feed-forward neural network. The algorithm has a precomputation step and a sampling step. While it generally requires…

We derive a method to efficiently compute the Green function of on arbitrary Hamiltonians defined on semi-infinite and periodic quasi-one-dimensional lattices. Computing the Green function is the backbone of quantum transport, electronic…

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…

We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissection, sparsification and low-rank compression. After…