English
Related papers

Related papers: Symmetric general linear methods

200 papers

We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…

Quantum Physics · Physics 2012-11-02 Václav Potoček

This paper develops a new class of linearly implicit time integration schemes called Linearly-Implicit Runge-Kutta-W (LIRK-W) methods. These schemes are based on an implicit-explicit approach which does not require a splitting of the right…

Numerical Analysis · Mathematics 2016-11-22 Paul Tranquilli , Adrian Sandu , Hong Zhang

In this article, we derive fast and robust parallel-in-time preconditioned iterative methods for the all-at-once linear systems arising upon discretization of time-dependent PDEs. The discretization we employ is based on a Runge--Kutta…

Numerical Analysis · Mathematics 2023-04-25 Santolo Leveque , Luca Bergamaschi , Ángeles Martínez , John W. Pearson

Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…

Numerical Analysis · Mathematics 2024-04-22 Philipp Bader , Sergio Blanes , Fernando Casas , Nikita Kopylov , Enrique Ponsoda

This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…

Optimization and Control · Mathematics 2024-06-21 Guoyin Li , Boris Mordukhovich , Jiangxing Zhu

We give a generalisation of the Lenstra-Lenstra-Lov\'asz (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this…

Number Theory · Mathematics 2025-02-03 Beth Romano , Jack A. Thorne

Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…

Optimization and Control · Mathematics 2025-04-10 Hamed Taghavian , Jens Sjölund

We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Mirta S. Iriondo , Oscar A. Reula

We consider a type of hypothetical compound materials in which its refractive index in spatial distribution meet $n(-x)=-n^{*}(x)$, belonging to anti-parity-time (APT) symmetric structures. Additionally, we demand balanced real positive-…

Optics · Physics 2025-04-25 Jeng Yi Lee

In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their…

Optimization and Control · Mathematics 2020-04-07 Atal Narayan Sahu , Aritra Dutta , Aashutosh Tiwari , Peter Richtárik

Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…

Numerical Analysis · Mathematics 2025-02-12 Gayatri Čaklović , Thibaut Lunet , Sebastian Götschel , Daniel Ruprecht

This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1…

Numerical Analysis · Mathematics 2020-04-10 Adrian Sandu

A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric…

Condensed Matter · Physics 2010-12-01 Sergio Albeverio , Shao-Ming Fei

To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…

Data Structures and Algorithms · Computer Science 2022-05-27 Zheqi Shen , Zijin Wan , Yan Gu , Yihan Sun

We compare two kinds of unification problems: Asymmetric Unification and Disunification, which are variants of Equational Unification. Asymmetric Unification is a type of Equational Unification where the right-hand sides of the equations…

Logic in Computer Science · Computer Science 2017-10-09 Veena Ravishankar , Kimberly A. Gero , Paliath Narendran

Projective symmetry groups (PSG) are the mathematical tools which allow to list and classify mean-field spin liquids (SL) based on a parton construction. The seminal work of Wen and its subsequent extension to bosons by Wang and Vishwanath…

Strongly Correlated Electrons · Physics 2013-04-30 Laura Messio , Claire Lhuillier , Grégoire Misguich

We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…

Numerical Analysis · Mathematics 2021-02-12 Pouria Behnoudfar , Quanling Deng , Victor M. Calo

It is well known that symplectic Runge-Kutta and Partitioned Runge-Kutta methods exactly preserve {\em quadratic} first integrals (invariants of motion) of the system being integrated. While this property is often seen as a mere curiosity…

Numerical Analysis · Mathematics 2015-06-22 J. M. Sanz-Serna

Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure…

High Energy Physics - Theory · Physics 2011-10-11 T. S. Nyawelo , F. Riccioni , J. W. van Holten , S. Groot Nibbelink

Exponential Runge-Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge-Kutta methods are available in the literature up to order 4 only. The aim of this paper is to…

Classical Analysis and ODEs · Mathematics 2016-06-20 Vu Thai Luan , Alexander Ostermann