SUMMARY In 1907, Erhard Schmidt published a paper in which he introduced an
orthogonalization algorithm that has since become known as the classical Gram‐Schmidt …

Today's floating-point arithmetic landscape is broader than ever. While scientific computing
has traditionally used single precision and double precision floating-point arithmetics, half …

In this work we demonstrate that nonrandom mechanisms that lead to single-particle
localization may also lead to many-body localization, even in the absence of disorder. In …

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Eigenvalue problems are ubiquitous in engineering and science. This book presents a
unified theoretical development of the two most important classes of algorithms for solving …

We propose a solution to the problem of quickly and accurately predicting gravitational
waveforms within any given physical model. The method is relevant for both real-time …

Abstract Block Gram-Schmidt algorithms serve as essential kernels in many scientific
computing applications, but for many commonly used variants, a rigorous treatment of their …

The Lanczos algorithm is one of the most frequently used numerical methods for computing
a few eigenvalues (and eventually eigenvectors) of a large sparse symmetric matrix A. If the …

Reasoning about uncertain orientations is one of the core problems in many perception
tasks such as object pose estimation or motion estimation. In these scenarios, poor …

A randomized Gram--Schmidt algorithm is developed for orthonormalization of high-
dimensional vectors or QR factorization. The proposed process can be less computationally …