English
Related papers

Related papers: A note on Korobov lattice rules for integration of…

200 papers

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

Numerical Analysis · Mathematics 2025-07-22 Markus Bachmayr , Matthieu Dolbeault , Polina Sachsenmaier

Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…

Data Structures and Algorithms · Computer Science 2019-06-14 Madhur Tulsiani , Julia Wolf

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing…

Quantum Physics · Physics 2015-03-20 Austin G. Fowler , Adam C. Whiteside , Lloyd C. L. Hollenberg

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

Numerical Analysis · Mathematics 2025-02-05 Lucas Onisk , Malena Sabaté Landman

The main goal of the article is testing a new classification algorithm. To this end we apply it to a relevant problem of describing the integrable cases of a subclass of two-dimensional lattices. By imposing the cut-off conditions…

Exactly Solvable and Integrable Systems · Physics 2017-09-08 Ismagil Habibullin , Mariya Poptsova

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…

Data Structures and Algorithms · Computer Science 2023-06-22 Thorsten Wißmann , Ulrich Dorsch , Stefan Milius , Lutz Schröder

This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…

Numerical Analysis · Mathematics 2014-07-21 Markus Bachmayr , Wolfgang Dahmen

In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…

Optimization and Control · Mathematics 2018-11-27 Georgios Kotsalis , Guanghui Lan

The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…

Logic · Mathematics 2019-09-04 Kohtaro Tadaki

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Numerical Analysis · Mathematics 2016-05-18 Kookjin Lee , Howard C. Elman

Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…

Numerical Analysis · Mathematics 2024-01-30 Fernando V. Ravelo , Martin Schreiber , Pedro S. Peixoto

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Numerical Analysis · Mathematics 2014-03-17 Markus Bachmayr , Wolfgang Dahmen

This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…

Numerical Analysis · Mathematics 2021-11-12 Stéphane Gaudreault , Greg Rainwater , Mayya Tokman

State-of-the-art algorithms in lattice gauge theory typically rely heavily on detailed balance, which is an instrumental tool to prove the correct convergence of the Markov Chain Monte Carlo Algorithm. In this work, we investigate an…

High Energy Physics - Lattice · Physics 2024-02-05 Marina Krstic Marinkovic , Joao C. Pinto Barros

We consider Galerkin approximations of holomorphic Fredholm operator eigenvalue problems for which the operator values don't have the structure "coercive+compact". In this case the regularity (in sense of [O. Karma, Numer. Funct. Anal.…

Numerical Analysis · Mathematics 2019-08-15 Martin Halla

We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable…

Optimization and Control · Mathematics 2016-03-04 Assalé Adjé

A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus…

Numerical Analysis · Mathematics 2024-04-24 Onyekachi Emenike , Fred J. Hickernell , Peter Kritzer

A comprehensive overview of lattice rules and polynomial lattice rules is given for function spaces based on $\ell_p$ semi-norms. Good lattice rules and polynomial lattice rules are defined as those obtaining worst-case errors bounded by…

Numerical Analysis · Mathematics 2020-07-20 Dirk Nuyens

The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and…

Quantum Physics · Physics 2025-10-20 Yunfei Wang , Xin Jin , Junyu Liu

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

Numerical Analysis · Mathematics 2012-05-09 S. M. Abrarov , B. M. Quine