发布求助
文献互助 智能选刊 最新文献

Acta Numerica最新文献

筛选
英文 中文
Randomized numerical linear algebra: Foundations and algorithms 随机数值线性代数:基础和算法
IF 14.2 1区 数学
Acta Numerica Pub Date : 2020-05-01 DOI: 10.1017/S0962492920000021
P. Martinsson, J. Tropp
{"title":"Randomized numerical linear algebra: Foundations and algorithms","authors":"P. Martinsson, J. Tropp","doi":"10.1017/S0962492920000021","DOIUrl":"https://doi.org/10.1017/S0962492920000021","url":null,"abstract":"This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues. Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nyström approximation of positive semidefinite matrices, single-view (‘streaming’) algorithms, full rank-revealing factorizations, solvers for linear systems, and approximation of kernel matrices that arise in machine learning and in scientific computing.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"29 1","pages":"403 - 572"},"PeriodicalIF":14.2,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492920000021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57446663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 208
The numerics of phase retrieval 相位恢复的数值
IF 14.2 1区 数学
Acta Numerica Pub Date : 2020-04-13 DOI: 10.1017/S0962492920000069
A. Fannjiang, T. Strohmer
{"title":"The numerics of phase retrieval","authors":"A. Fannjiang, T. Strohmer","doi":"10.1017/S0962492920000069","DOIUrl":"https://doi.org/10.1017/S0962492920000069","url":null,"abstract":"Phase retrieval, i.e. the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications, such as X-ray crystallography, diffraction imaging, optics, quantum mechanics and astronomy. This problem has confounded engineers, physicists, and mathematicians for many decades. Recently, phase retrieval has seen a resurgence in research activity, ignited by new imaging modalities and novel mathematical concepts. As our scientific experiments produce larger and larger datasets and we aim for faster and faster throughput, it is becoming increasingly important to study the involved numerical algorithms in a systematic and principled manner. Indeed, the past decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval. In this paper we will review these recent advances from a numerical viewpoint.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"29 1","pages":"125 - 228"},"PeriodicalIF":14.2,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492920000069","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41678878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 66
Numerical methods for nonlocal and fractional models 非局部和分数模型的数值方法
IF 14.2 1区 数学
Acta Numerica Pub Date : 2020-02-01 DOI: 10.2172/1598758
M. D'Elia, Q. Du, Christian A. Glusa, M. Gunzburger, Xiaochuan Tian, Zhi Zhou
{"title":"Numerical methods for nonlocal and fractional models","authors":"M. D'Elia, Q. Du, Christian A. Glusa, M. Gunzburger, Xiaochuan Tian, Zhi Zhou","doi":"10.2172/1598758","DOIUrl":"https://doi.org/10.2172/1598758","url":null,"abstract":"Partial differential equations (PDEs) are used with huge success to model phenomena across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDEs fail to adequately model observed phenomena, or are not the best available model for that purpose. On the other hand, in many situations, nonlocal models that account for interaction occurring at a distance have been shown to more faithfully and effectively model observed phenomena that involve possible singularities and other anomalies. In this article we consider a generic nonlocal model, beginning with a short review of its definition, the properties of its solution, its mathematical analysis and of specific concrete examples. We then provide extensive discussions about numerical methods, including finite element, finite difference and spectral methods, for determining approximate solutions of the nonlocal models considered. In that discussion, we pay particular attention to a special class of nonlocal models that are the most widely studied in the literature, namely those involving fractional derivatives. The article ends with brief considerations of several modelling and algorithmic extensions, which serve to show the wide applicability of nonlocal modelling.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"29 1","pages":"1 - 124"},"PeriodicalIF":14.2,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44856694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 117
Computing quantum dynamics in the semiclassical regime 半经典区域中的量子动力学计算
IF 14.2 1区 数学
Acta Numerica Pub Date : 2020-02-01 DOI: 10.1017/S0962492920000033
C. Lasser, C. Lubich
{"title":"Computing quantum dynamics in the semiclassical regime","authors":"C. Lasser, C. Lubich","doi":"10.1017/S0962492920000033","DOIUrl":"https://doi.org/10.1017/S0962492920000033","url":null,"abstract":"The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn’s semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"29 1","pages":"229 - 401"},"PeriodicalIF":14.2,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492920000033","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46197333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 58
Approximation algorithms in combinatorial scientific computing 组合科学计算中的近似算法
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000035
A. Pothen, S. Ferdous, F. Manne
{"title":"Approximation algorithms in combinatorial scientific computing","authors":"A. Pothen, S. Ferdous, F. Manne","doi":"10.1017/S0962492919000035","DOIUrl":"https://doi.org/10.1017/S0962492919000035","url":null,"abstract":"We survey recent work on approximation algorithms for computing degree-constrained subgraphs in graphs and their applications in combinatorial scientific computing. The problems we consider include maximization versions of cardinality matching, edge-weighted matching, vertex-weighted matching and edge-weighted $b$ -matching, and minimization versions of weighted edge cover and $b$ -edge cover. Exact algorithms for these problems are impractical for massive graphs with several millions of edges. For each problem we discuss theoretical foundations, the design of several linear or near-linear time approximation algorithms, their implementations on serial and parallel computers, and applications. Our focus is on practical algorithms that yield good performance on modern computer architectures with multiple threads and interconnected processors. We also include information about the software available for these problems.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"541 - 633"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45877211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Numerical analysis of hemivariational inequalities in contact mechanics 接触力学中半变分不等式的数值分析
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000023
W. Han, M. Sofonea
{"title":"Numerical analysis of hemivariational inequalities in contact mechanics","authors":"W. Han, M. Sofonea","doi":"10.1017/S0962492919000023","DOIUrl":"https://doi.org/10.1017/S0962492919000023","url":null,"abstract":"Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"175 - 286"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46932286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 81
ANU volume 28 Cover and Back matter 澳大利亚国立大学第28卷封面和封底
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/s0962492919000084
{"title":"ANU volume 28 Cover and Back matter","authors":"","doi":"10.1017/s0962492919000084","DOIUrl":"https://doi.org/10.1017/s0962492919000084","url":null,"abstract":"","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"b1 - b2"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0962492919000084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48842143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ANU volume 28 Cover and Front matter 澳大利亚国立大学第28卷封面和封面
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/s0962492919000072
{"title":"ANU volume 28 Cover and Front matter","authors":"","doi":"10.1017/s0962492919000072","DOIUrl":"https://doi.org/10.1017/s0962492919000072","url":null,"abstract":"","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"f1 - f7"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0962492919000072","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46012381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving inverse problems using data-driven models 使用数据驱动模型求解逆问题
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000059
S. Arridge, P. Maass, O. Öktem, C. Schönlieb
{"title":"Solving inverse problems using data-driven models","authors":"S. Arridge, P. Maass, O. Öktem, C. Schönlieb","doi":"10.1017/S0962492919000059","DOIUrl":"https://doi.org/10.1017/S0962492919000059","url":null,"abstract":"Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"1 - 174"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42196723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 415
Numerical methods for Kohn–Sham density functional theory Kohn-Sham密度泛函理论的数值方法
IF 14.2 1区 数学
Acta Numerica Pub Date : 2019-05-01 DOI: 10.1017/S0962492919000047
Lin Lin, Jianfeng Lu, Lexing Ying
{"title":"Numerical methods for Kohn–Sham density functional theory","authors":"Lin Lin, Jianfeng Lu, Lexing Ying","doi":"10.1017/S0962492919000047","DOIUrl":"https://doi.org/10.1017/S0962492919000047","url":null,"abstract":"Kohn–Sham density functional theory (DFT) is the most widely used electronic structure theory. Despite significant progress in the past few decades, the numerical solution of Kohn–Sham DFT problems remains challenging, especially for large-scale systems. In this paper we review the basics as well as state-of-the-art numerical methods, and focus on the unique numerical challenges of DFT.","PeriodicalId":48863,"journal":{"name":"Acta Numerica","volume":"28 1","pages":"405 - 539"},"PeriodicalIF":14.2,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0962492919000047","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43079969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书