Parallel Preconditioned Eigenvalue and Singular Value Solvers

并行预条件特征值和奇异值求解器

基本信息

项目摘要

This award, from the computational mathematics program of the Division of Mathematical Sciences, supports the research of the principal investigator, which covers a balanced mix of theoretical investigations, software support and development, and advances for modern applications. The research focuses on design of new efficient robust parallel preconditioned methods for interior eigenvalue and singular value computations. The main emphasis is on the following challenging issues: investigating availability and efficiency of preconditioning; avoiding the folded spectrum approach, analyzing the possibility of computing the singular values of an operator using preconditioning; and establishing convergence theory for novel iterative solvers. For the latter, a novel application of classical majorization theory permits analysis of the convergence behavior of block eigenvalue and singular value solvers. This work is also relevant for applications; the singular vectors, corresponding to the largest singular values of a matrix are used for performing the principal component analysis of data described by a data matrix. Here the focus is on multi-dimensional image segmentation.The topic of this research is motivated by the fact that the class of problems under consideration describes many phenomena in physics and mechanics, and for practical calculations may require extreme computational power. Advances in the computational approaches can provide noticeable improvements in the accuracy and efficiency of calculations. Implementing the developments in publicly available software enhances the potential for significant broader impact, due to the relevance of the software for a large range of applications. The application specifically targeted by the PI is image segmentation, such as occurs in tracking moving objects in videos. Additional impact of the project is on graduate student training. The research of the PI provides an opportunity to train students in important computational research motivated by real practical applications.
该奖项来自数学科学部的计算数学项目,支持首席研究员的研究,该研究涵盖了理论研究、软件支持和开发以及现代应用进展的平衡组合。研究的重点是设计一种新的高效、稳健的并行预条件方法,用于内部特征值和奇异值的计算。主要集中在以下具有挑战性的问题上:研究预条件的有效性和效率;避免使用折叠谱方法;分析使用预条件计算算子奇异值的可能性;以及建立新的迭代求解器的收敛理论。对于后者,经典优化理论的新应用允许分析块本征值和奇异值求解器的收敛行为。这项工作也与应用相关;对应于矩阵的最大奇异值的奇异向量被用于执行由数据矩阵描述的数据的主成分分析。这里的重点是多维图像分割。这项研究的主题是因为所考虑的问题类描述了许多物理和力学中的现象,对于实际计算可能需要极大的计算能力。计算方法的进步可以显著提高计算的准确性和效率。由于软件与大范围的应用程序相关,在可公开获得的软件中实施开发增强了产生重大更广泛影响的可能性。PI专门针对的应用是图像分割,例如在跟踪视频中的运动对象时发生的图像分割。该项目还对研究生培训产生了影响。PI的研究提供了一个机会,以培养学生在实际应用中推动的重要计算研究。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

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

Julien Langou的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ 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:
    $ 18万
  • 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:
    $ 18万
  • 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:
    $ 18万
  • 项目类别:
    Continuing Grant
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
  • 批准号:
    1054864
  • 财政年份:
    2011
  • 资助金额:
    $ 18万
  • 项目类别:
    Continuing 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:
    $ 18万
  • 项目类别:
    Standard 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:
    $ 18万
  • 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:
    $ 18万
  • 项目类别:
    Standard Grant

相似海外基金

Robust Preconditioned Gradient Descent Algorithms for Deep Learning
用于深度学习的鲁棒预条件梯度下降算法
  • 批准号:
    2208314
  • 财政年份:
    2022
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Advances in Scalable Iterative Solvers: Multilevel, Nonlinearly Preconditioned, and Parallel-in-Time
可扩展迭代求解器的进展:多级、非线性预处理和时间并行
  • 批准号:
    RGPIN-2019-04155
  • 财政年份:
    2022
  • 资助金额:
    $ 18万
  • 项目类别:
    Discovery Grants Program - Individual
Quantifying VN Antibodies of BRD-causing Viruses in Preconditioned Calves Using V
使用 V 定量预处理犊牛中引起 BRD 的病毒的 VN 抗体
  • 批准号:
    574787-2022
  • 财政年份:
    2022
  • 资助金额:
    $ 18万
  • 项目类别:
    University Undergraduate Student Research Awards
Advances in Scalable Iterative Solvers: Multilevel, Nonlinearly Preconditioned, and Parallel-in-Time
可扩展迭代求解器的进展:多级、非线性预处理和时间并行
  • 批准号:
    RGPIN-2019-04155
  • 财政年份:
    2021
  • 资助金额:
    $ 18万
  • 项目类别:
    Discovery Grants Program - Individual
Renal repair effects of senolytic preconditioned mesenchymal stromal cells in diabetic kidney disease
senolytic 预处理间充质基质细胞对糖尿病肾病的肾修复作用
  • 批准号:
    10170555
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
Netrin-1 and Netrin-1 Preconditioned EPCs in Vascular Protection
Netrin-1 和 Netrin-1 预处理 EPC 在血管保护中的作用
  • 批准号:
    10557815
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
Renal repair effects of senolytic preconditioned mesenchymal stromal cells in diabetic kidney disease
senolytic 预处理间充质基质细胞对糖尿病肾病的肾修复作用
  • 批准号:
    10200246
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
Netrin-1 and Netrin-1 Preconditioned EPCs in Vascular Protection
Netrin-1 和 Netrin-1 预处理 EPC 在血管保护中的作用
  • 批准号:
    10361442
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
Renal repair effects of senolytic preconditioned mesenchymal stromal cells in diabetic kidney disease
senolytic 预处理间充质基质细胞对糖尿病肾病的肾修复作用
  • 批准号:
    10092153
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
Therapeutic strategy of hypoxia preconditioned microglia for vascular dementia
缺氧预处理小胶质细胞治疗血管性痴呆的治疗策略
  • 批准号:
    20K22683
  • 财政年份:
    2020
  • 资助金额:
    $ 18万
  • 项目类别:
    Grant-in-Aid for Research Activity Start-up
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了