Locally Optimal Preconditioned Eigenvalue Solvers

局部最优预条件特征值求解器

基本信息

项目摘要

The area of preconditioned iterative solvers for eigenvalue computations is rapidly developing. Software implementations of several preconditioned eigensolvers, in particular, the locally optimal block preconditioned conjugate gradient (LOBPCG) method developed by the principal investigator (PI) earlier, are being written. The recent progress opens new opportunities to develop efficient preconditioned iterative solvers for interior eigenvalues and singular value computations. The use of preconditioned eigensolvers in applications raises new area-specific important issues, both practical and theoretical, which need to be resolved. The proposed research addresses these issues based on the success of the previous work of the PI. The PI expects to advance the theory of some known methods, to discover new locally optimal algorithms, and to be able to provide specific recommendations concerning the choice of methods. The following specific and interrelated research projects areproposed: reducing the LOBPCG costs for large block sizes; developing efficient preconditioned solvers for interior eigenvalues and singular value computations; finite element method error analysis for eigenproblems resulting from partial differential equations with highly discontinuous coefficients. The projects form a balanced mix of theoretical research and code development. Numerical simulations are to be performed on modern parallel computing systems, such as the IBM BlueGene/L supercomputer.The ideas behind the proposed research are original, and build on prior work. The project addresses mathematically difficult and practically important problems. The broader impact resulting from the proposed activity is twofold: Ph.D. education and advances in software. Funds are requested in the proposal to support Ph.D. students. Improvement of the software currently used and development of new codes for scientists and engineers creates potential advances, e.g., in analyzing extremely large data sets, which is important for national security.
用于特征值计算的预条件迭代求解器的领域正在迅速发展。正在编写几个预条件特征解算器的软件实现,特别是由主要研究者(PI)先前开发的局部最优块预条件共轭梯度(LOBPCG)方法。最近的进展为开发高效的内特征值和奇异值计算的预条件迭代求解器提供了新的机会。预条件特征解析器在应用中的使用提出了新的领域特定的重要问题,无论是实践上还是理论上,都需要解决。拟议的研究在国际和平研究所以前工作取得成功的基础上解决了这些问题。PI期望发展一些已知方法的理论,发现新的局部最优算法,并能够提供关于方法选择的具体建议。提出了以下具体和相关的研究项目:降低大块大小的LOBPCG成本;开发高效的内部特征值和奇异值计算的预条件求解器;针对具有高度间断系数的偏微分方程组的特征问题进行有限元误差分析。这些项目形成了理论研究和代码开发的平衡组合。数值模拟将在现代并行计算系统上进行,如IBM Bluegene/L超级计算机。拟议研究背后的想法是原创的,并建立在先前工作的基础上。该项目解决了数学上的困难和实际中的重要问题。拟议活动产生的更广泛的影响是双重的:博士教育和软件进步。提案中要求提供资金来支持博士生。目前使用的软件的改进和科学家和工程师新代码的开发带来了潜在的进步,例如,在分析对国家安全至关重要的超大数据集方面。

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 }}

Andrew Knyazev其他文献

Andrew Knyazev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('Andrew Knyazev', 18)}}的其他基金

Analysis of Microarray Gene Expression Data
微阵列基因表达数据分析
  • 批准号:
    0728941
  • 财政年份:
    2007
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Preconditioned Algorithms for Large Eigenvalue Problems
大特征值问题的预处理算法
  • 批准号:
    0208773
  • 财政年份:
    2002
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Sixth IMACS International Symposium on Iterative Methods in Scientific Computing; March 27-30, 2003, Denver, CO
第六届 IMACS 科学计算迭代方法国际研讨会;
  • 批准号:
    0209311
  • 财政年份:
    2002
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Acquisition of a High-Performance Parallel Computer for Mathematical Sciences and Applications
获取用于数学科学和应用的高性能并行计算机
  • 批准号:
    0079719
  • 财政年份:
    2000
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Preconditioned Parallel Methods for Large Symmetric Eigenproblems
数学科学:大型对称本征问题的预处理并行方法
  • 批准号:
    9501507
  • 财政年份:
    1995
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant

相似海外基金

Optimal utility-based design of oncology clinical development programmes
基于效用的肿瘤学临床开发项目的优化设计
  • 批准号:
    2734768
  • 财政年份:
    2026
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Studentship
Optimal cell factories for membrane protein production
用于膜蛋白生产的最佳细胞工厂
  • 批准号:
    BB/Y007603/1
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Research Grant
Hybrid AI and multiscale physical modelling for optimal urban decarbonisation combating climate change
混合人工智能和多尺度物理建模,实现应对气候变化的最佳城市脱碳
  • 批准号:
    EP/X029093/1
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Fellowship
Collaborative Research: Mechanics of Optimal Biomimetic Torene Plates and Shells with Ultra-high Genus
合作研究:超高属度最优仿生Torene板壳力学
  • 批准号:
    2323415
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Conference: Supplementary funding for the BIRS-CMO workshop Optimal Transport and Dynamics (24s5198)
会议:BIRS-CMO 研讨会最佳运输和动力学的补充资金 (24s5198)
  • 批准号:
    2401019
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
CAREER: Statistical Power Analysis and Optimal Sample Size Planning for Longitudinal Studies in STEM Education
职业:STEM 教育纵向研究的统计功效分析和最佳样本量规划
  • 批准号:
    2339353
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Continuing Grant
CAREER: Optimal Transport Beyond Probability Measures for Robust Geometric Representation Learning
职业生涯:超越概率测量的最佳传输以实现稳健的几何表示学习
  • 批准号:
    2339898
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Continuing Grant
Labor Market Polarization, Earnings Inequality and Optimal Tax Progressivity: A Theoretical and Empirical Analysis
劳动力市场两极分化、收入不平等和最优税收累进性:理论与实证分析
  • 批准号:
    24K04909
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Collaborative Research: Integrating Optimal Function and Compliant Mechanisms for Ubiquitous Lower-Limb Powered Prostheses
合作研究:将优化功能和合规机制整合到无处不在的下肢动力假肢中
  • 批准号:
    2344765
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
Collaborative Research: Can Irregular Structural Patterns Beat Perfect Lattices? Biomimicry for Optimal Acoustic Absorption
合作研究:不规则结构模式能否击败完美晶格?
  • 批准号:
    2341950
  • 财政年份:
    2024
  • 资助金额:
    $ 24.95万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了