A review of the present status, recent enhancements, and applicability of the S iesta program
is presented. Since its debut in the mid-1990s, S iesta's flexibility, efficiency, and free …

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic
structure theory and many other areas of computational science. The computational effort …

DFTB+ is a versatile community developed open source software package offering fast and
efficient methods for carrying out atomistic quantum mechanical simulations. By …

In this paper we propose a new method for the iterative computation of a few of the extremal
eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based …

This paper sketches the main research developments in the area of computational methods
for eigenvalue problems during the 20th century. The earliest of such methods dates back to …

The evolution of digital libraries and the Internet has dramatically transformed the
processing, storage, and retrieval of information. Efforts to digitize text, images, video, and …

We study the ℓ1-low rank approximation problem, where for a given nxd matrix A and
approximation factor α≤ 1, the goal is to output a rank-k matrix  for which‖ A-Â‖ 1≤ α …

The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian)
matrix is an important subtask in many contexts, for example in electronic structure …

We consider relative error low rank approximation of tensors with respect to the Frobenius
norm. Namely, given an order-q tensor A∊ ℝ∏ i= 1 q ni, output a rank-k tensor B for which …

This paper studies the Principal Component Analysis (PCA) problem in the distributed and
streaming models of computation. Given a matrix A∈ R m× n, a rank parameter k< rank (A) …