Gram‐Schmidt orthogonalization: 100 years and more

SJ Leon, Å Björck, W Gander - Numerical Linear Algebra with …, 2013 - Wiley Online Library
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 …

Mixed precision algorithms in numerical linear algebra

NJ Higham, T Mary - Acta Numerica, 2022 - cambridge.org
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 …

From Bloch oscillations to many-body localization in clean interacting systems

E van Nieuwenburg, Y Baum… - Proceedings of the …, 2019 - National Acad Sciences
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 …

GMRES algorithms over 35 years

Q Zou - Applied Mathematics and Computation, 2023 - Elsevier
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 …

[图书][B] The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods

DS Watkins - 2007 - SIAM
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 …

Fast prediction and evaluation of gravitational waveforms using surrogate models

SE Field, CR Galley, JS Hesthaven, J Kaye, M Tiglio - Physical Review X, 2014 - APS
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 …

Block Gram-Schmidt algorithms and their stability properties

E Carson, K Lund, M Rozložník, S Thomas - Linear Algebra and its …, 2022 - Elsevier
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 …

[图书][B] The Lanczos and conjugate gradient algorithms: from theory to finite precision computations

G Meurant - 2006 - SIAM
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 …

Deep orientation uncertainty learning based on a bingham loss

I Gilitschenski, R Sahoo, W Schwarting… - International …, 2019 - openreview.net
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 …

Randomized Gram--Schmidt process with application to GMRES

O Balabanov, L Grigori - SIAM Journal on Scientific Computing, 2022 - SIAM
A randomized Gram--Schmidt algorithm is developed for orthonormalization of high-
dimensional vectors or QR factorization. The proposed process can be less computationally …