English
Related papers

Related papers: Theory of large-scale matrix computation and appli…

200 papers

We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…

Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16)…

Numerical Analysis · Mathematics 2025-05-28 Kengo Suzuki , Takeshi Iwashita

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for…

Strongly Correlated Electrons · Physics 2016-12-21 A. Nocera , G. Alvarez

We propose herein an extension of truncated spectrum methodologies (TSMs), a non-perturbative numerical approach able to elucidate the low energy properties of quantum field theories. TSMs, in their various flavors, involve a division of a…

High Energy Physics - Theory · Physics 2023-08-02 Márton K. Lájer , Robert M. Konik

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

Quantum Physics · Physics 2022-05-18 Alexis Ralli , Michael I. Williams , Peter V. Coveney

Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…

Numerical Analysis · Mathematics 2021-11-09 Keiichi Morikuni

Low-rank Krylov methods are one of the few options available in the literature to address the numerical solution of large-scale general linear matrix equations. These routines amount to well-known Krylov schemes that have been equipped with…

Numerical Analysis · Mathematics 2020-01-28 Davide Palitta , Patrick Kürschner

In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…

Materials Science · Physics 2020-04-15 Igor Ying Zhang , Andreas Grüneis

We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [arXiv:2111.06665] in electronic…

Chemical Physics · Physics 2023-04-04 Gero Friesecke , Gergely Barcza , Örs Legeza

High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…

Numerical Analysis · Mathematics 2018-01-16 Yassine Boubendir , Fatih Ecevit , Fernando Reitich

The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to…

Computational Physics · Physics 2020-02-19 Minjung Kim , Glenn J. Martyna , Sohrab Ismail-Beigi

We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon…

High Energy Physics - Lattice · Physics 2011-02-01 Jacques C. R. Bloch , Simon Heybrock

Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the…

Numerical Analysis · Mathematics 2019-12-30 Volker Grimm

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological…

Astrophysics · Physics 2009-11-13 K. Dolag , S. Borgani , S. Schindler , A. Diaferio , A. M. Bykov

Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…

Quantum Physics · Physics 2016-10-25 Nicholas C. Rubin

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…

Soft Condensed Matter · Physics 2007-05-23 Wilfried Wunderlich

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…

Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…

Materials Science · Physics 2009-11-11 Florian R. Krajewski , Michele Parrinello

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…

Numerical Analysis · Mathematics 2021-10-05 Joel A. Tropp

In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data processing techniques. Owing to these new exciting…

Information Theory · Computer Science 2020-04-22 Tamir Bendory , Alberto Bartesaghi , Amit Singer