CAREER: Foundations for Understanding and Reaching the Limits of Standard Numerical Linear Algebra
职业:理解和达到标准数值线性代数极限的基础
基本信息
- 批准号:1054864
- 负责人:
- 金额:$ 40万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-02-01 至 2017-01-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Faster numerical simulations are critical, for example, in basic science for enabling novel scientific discoveries, or in engineering for developing revolutionary new products. Most research in this vein aims to develop new algorithmitic implementations to accelerate computations. Rather than moving down that path, this research first answers the question: "by how much can we accelerate a given computation?" The second component, then, is to develop highly-efficient algorithms able to reach these minimum time limits. Our research leads to a better understanding of our algorithms and their intrinsic limitations, and eventually results in better, near-optimal algorithms. Both components of this research represent tremendous challenges given the complexity of the current computing architecture and the problem to be solved.The results of this research will be communicated in an integrated education component of this project in which previous and recent work and methodologies are disseminated through classes, the publication of a book, the distribution of source codes and the development of web documents. Important taxonomy and bibliographic work will be performed during interdisciplinary math/CS reading classes. Broader outreach activities are conducted in K-12 classrooms and through public STEM- related events in the metropolitan Denver area.The research in the project includes three components. Given a numerical problem to be solved, the investigator (1) develops an ad-hoc model detailing the theoretical limitations of the computational machine, (2) simulates the execution of an algorithm based on the ad-hoc model, and (3) conducts numerical experiments on the targeted architecture. The investigator's methodology applies iterate improvements between these three components until they match. Each improvement requires answering several open questions in terms of lower bounds and algorithms.
例如,在实现新的科学发现的基础科学中,或在开发革命性新产品的工程中,更快的数值模拟是至关重要的。这方面的大部分研究都旨在开发新的算法实现来加速计算。这项研究并没有沿着这条路走下去,而是首先回答了这个问题:“我们可以将给定的计算加速多少?”然后,第二个组成部分是开发能够达到这些最小时间限制的高效算法。我们的研究使我们更好地理解了我们的算法及其内在局限性,并最终产生了更好的、接近最优的算法。考虑到当前计算架构的复杂性和需要解决的问题,这项研究的两个部分都代表着巨大的挑战。这项研究的结果将在该项目的一个综合教育部分中传播,在该部分中,以前和最近的工作和方法通过课堂、出版一本书、分发源代码和开发网络文档来传播。重要的分类学和书目工作将在跨学科的数学/CS阅读课上进行。在丹佛市的K-12教室和与STEM相关的公共活动中,开展了更广泛的外展活动。给定一个要解决的数值问题,调查者(1)开发了一个特别模型,详细说明了计算机器的理论限制,(2)模拟了基于特别模型的算法的执行,以及(3)在目标体系结构上进行了数值实验。研究人员的方法在这三个组成部分之间进行迭代改进,直到它们匹配为止。每一次改进都需要回答几个关于下界和算法的开放问题。
项目成果
期刊论文数量(0)
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会议论文数量(0)
专利数量(0)
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Julien Langou其他文献
Tightening I/O Lower Bounds through the Hourglass Dependency Pattern
通过沙漏依赖模式收紧 I/O 下限
- DOI:
10.1145/3626183.3659986 - 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Lionel Eyraud;Guillaume Iooss;Julien Langou;Fabrice Rastello - 通讯作者:
Fabrice Rastello
Julien Langou的其他文献
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{{ truncateString('Julien Langou', 18)}}的其他基金
Collaborative Research: Frameworks: Basic ALgebra LIbraries for Sustainable Technology with Interdisciplinary Collaboration (BALLISTIC)
协作研究:框架:跨学科协作可持续技术的基本代数库(BALLISTIC)
- 批准号:
2004850 - 财政年份:2020
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
SHF: EAGER: Developing General Techniques for Tightening Bounds of the Data-Movement Complexity of Large Scale Parallel Applications
SHF:EAGER:开发通用技术来收紧大规模并行应用程序的数据移动复杂性的界限
- 批准号:
1645514 - 财政年份:2016
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
SI2-SSI: Collaborative Research: Sustained Innovation for Linear Algebra Software (SILAS)
SI2-SSI:协作研究:线性代数软件 (SILAS) 的持续创新
- 批准号:
1339797 - 财政年份:2013
- 资助金额:
$ 40万 - 项目类别:
Continuing Grant
Parallel Preconditioned Eigenvalue and Singular Value Solvers
并行预条件特征值和奇异值求解器
- 批准号:
1115734 - 财政年份:2011
- 资助金额:
$ 40万 - 项目类别:
Continuing Grant
Collaborative Research: SDCI HPC Improvement: Improvement and Support of Community Based Dense Linear Algebra Software for Extreme Scale Computational Science
合作研究:SDCI HPC 改进:针对超大规模计算科学的基于社区的密集线性代数软件的改进和支持
- 批准号:
1032861 - 财政年份:2010
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
II-NEW: GPU Cluster for Computing Research
II-新:用于计算研究的 GPU 集群
- 批准号:
0958354 - 财政年份:2010
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Collaborative CPA-ACR-T: PLASMA: Parallel Linear Algebra Software for Multiprocessor Architectures.
协作 CPA-ACR-T:PLASMA:用于多处理器架构的并行线性代数软件。
- 批准号:
0811520 - 财政年份:2008
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
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