Related papers: Exact computations with quasiseparable matrices

This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…

Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…

Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…

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…

In an iterative approach for solving linear systems with ill-conditioned, symmetric positive definite (SPD) kernel matrices, both fast matrix-vector products and fast preconditioning operations are required. Fast (linear-scaling)…

One of the most common, but at the same time expensive operations in linear algebra, is multiplying two matrices $A$ and $B$. With the rapid development of machine learning and increases in data volume, performing fast matrix intensive…

A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…

Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…

Hashing method maps similar data to binary hashcodes with smaller hamming distance, and it has received a broad attention due to its low storage cost and fast retrieval speed. However, the existing limitations make the present algorithms…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

We study the exactness of the semidefinite programming (SDP) relaxation of quadratically constrained quadratic programs (QCQPs). With the aggregate sparsity matrix from the data matrices of a QCQP with $n$ variables, the rank and positive…

In this paper, we present two fast matrix representation algorithms based on the recursive decomposition of multivectors into specific right and left ideals. We also examine the relation between these two representations. Furthermore, we…

Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…

Classes of set functions along with a choice of ground set are a bedrock to determine and develop corresponding variants of greedy algorithms to obtain efficient solutions for combinatorial optimization problems. The class of approximate…

Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…

We show how to adapt the quasi-Newton method to the electronic-structure calculations using systematic basis sets. Our implementation requires less iterations than the conjugate gradient method, while the computational cost per iteration is…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

We present an efficient computational representation of central simple algebras using Brauer factor sets. Using this representation and polynomial quantum algorithms for number theoretical tasks such as factoring and $S$-unit group…