CAREER: Numerical Linear Algebra, Random Matrix Theory and Applications

职业:数值线性代数、随机矩阵理论及应用

基本信息

  • 批准号:
    1945652
  • 负责人:
  • 金额:
    $ 43.24万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2019
  • 资助国家:
    美国
  • 起止时间:
    2019-07-01 至 2023-06-30
  • 项目状态:
    已结题

项目摘要

Numerical algorithms are pervasive in our lives today.  These algorithms are used, for example, to send data to mobile devices and to simulate fire and water in movies.  Many of the most classical algorithms, and particularly those with applications in linear algebra, have been extremely useful for decades, if not centuries.  Yet, some of these algorithms are poorly understood -- they can fail catastrophically, but rarely do.  In other words, the worst-case behavior is poor, but the average-case behavior is good.  This research will advance the understanding of this phenomenon by employing techniques from the ever-expanding field of random matrix theory (RMT).  In turn, this research gives rise to new questions within RMT. A substantial feature of this project is the extensive educational component that integrates research and education. This integration is achieved via a three-pronged approach including a summer workshop on random matrices, high school engagement, and undergraduate/graduate student mentoring.Two natural ways to employ RMT within numerical linear algebra also coincide with the two most common themes in numerical linear algebra: Algorithm analysis and algorithm development. For example, remarkably detailed estimates from RMT such as rigidity and edge universality have found concrete applications within numerical linear algebra giving average-case performance for the classical power method. Randomized algorithms have found great utility in the big-data age.  This research will employ both of these themes with applications to data science, psychology and beyond.  The synergy of the fields of RMT and numerical linear algebra provides a unique educational opportunity for graduate, undergraduate and high school students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
数值算法在我们今天的生活中无处不在。例如,这些算法被用来向移动的设备发送数据,以及在电影中模拟火和水。许多最经典的算法,特别是那些在线性代数中应用的算法,几十年来,如果不是几个世纪的话,都非常有用。然而,其中一些算法却知之甚少--它们可能会灾难性地失败,但很少这样做。换句话说,最坏情况下的行为是差的,但平均情况下的行为是好的。这项研究将通过采用来自不断扩展的随机矩阵理论(RMT)领域的技术来促进对这种现象的理解。反过来,这项研究在RMT中产生了新的问题。该项目的一个重要特点是将研究和教育结合起来的广泛的教育部分。这种整合是通过三管齐下的方法实现的,包括关于随机矩阵的夏季研讨会,高中参与和本科生/研究生指导。在数值线性代数中使用RMT的两种自然方式也符合数值线性代数中最常见的两个主题:算法分析和算法开发。例如,从RMT非常详细的估计,如刚性和边缘的普遍性,发现具体的应用在数值线性代数中给出平均情况下的经典功率方法的性能。随机算法在大数据时代有很大的用处。这项研究将利用这两个主题与应用到数据科学,心理学和超越。RMT和数值线性代数领域的协同作用为研究生提供了一个独特的教育机会,该奖项反映了NSF的法定使命,并通过使用基金会的学术价值和更广泛的影响审查标准。

项目成果

期刊论文数量(17)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Analysis of stochastic Lanczos quadrature for spectrum approximation
谱近似的随机Lanczos求积分析
A Probabilistic Analysis of the Neumann Series Iteration
诺依曼级数迭代的概率分析
On numerical inverse scattering for the Korteweg–de Vries equation with discontinuous step-like data
具有不连续阶梯状数据的 Korteweg–de Vries 方程的数值逆散射
  • DOI:
    10.1088/1361-6544/ab6c37
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    1.7
  • 作者:
    Bilman, Deniz;Trogdon, Thomas
  • 通讯作者:
    Trogdon, Thomas
Universality in numerical computation with random data: Case studies and analytical results
随机数据数值计算的普遍性:案例研究和分析结果
  • DOI:
    10.1063/1.5117151
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    1.3
  • 作者:
    Deift, Percy;Trogdon, Thomas
  • 通讯作者:
    Trogdon, Thomas
On spectral and numerical properties of random butterfly matrices
  • DOI:
    10.1016/j.aml.2019.03.024
  • 发表时间:
    2017-09
  • 期刊:
  • 影响因子:
    0
  • 作者:
    T. Trogdon
  • 通讯作者:
    T. Trogdon
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Thomas Trogdon其他文献

Numerical Solution of Riemann–Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials
  • DOI:
    10.1007/s00365-013-9221-3
  • 发表时间:
    2013-12-11
  • 期刊:
  • 影响因子:
    1.200
  • 作者:
    Sheehan Olver;Thomas Trogdon
  • 通讯作者:
    Thomas Trogdon

Thomas Trogdon的其他文献

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{{ truncateString('Thomas Trogdon', 18)}}的其他基金

Collaborative Research: Random Matrices and Algorithms in High Dimension
合作研究:高维随机矩阵和算法
  • 批准号:
    2306438
  • 财政年份:
    2023
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Continuing Grant
CAREER: Numerical Linear Algebra, Random Matrix Theory and Applications
职业:数值线性代数、随机矩阵理论及应用
  • 批准号:
    1753185
  • 财政年份:
    2018
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Continuing Grant
CBMS Conference: The Solution of Problems in Multiply-Connected Domains
CBMS会议:多连通域问题的解决方案
  • 批准号:
    1743920
  • 财政年份:
    2017
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    1303018
  • 财政年份:
    2013
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Fellowship Award

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CAREER: Theoretical and Computational Advances for Enabling Robust Numerical Guarantees in Linear and Mixed Integer Programming Solvers
职业:在线性和混合整数规划求解器中实现鲁棒数值保证的理论和计算进展
  • 批准号:
    2340527
  • 财政年份:
    2024
  • 资助金额:
    $ 43.24万
  • 项目类别:
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DMS-EPSRC: Certifying Accuracy of Randomized Algorithms in Numerical Linear Algebra
DMS-EPSRC:验证数值线性代数中随机算法的准确性
  • 批准号:
    EP/Y030990/1
  • 财政年份:
    2024
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Research Grant
DMS-EPSRC:Certifying Accuracy of Randomized Algorithms in Numerical Linear Algebra
DMS-EPSRC:验证数值线性代数中随机算法的准确性
  • 批准号:
    2313434
  • 财政年份:
    2023
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
Collaborative Research: Elements: A Cyberlaboratory for Randomized Numerical Linear Algebra
合作研究:Elements:随机数值线性代数网络实验室
  • 批准号:
    2309445
  • 财政年份:
    2023
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
RUI: The Non-Linear Universe: Precision Numerical Cosmology and Fundamental Physics
RUI:非线性宇宙:精确数值宇宙学和基础物理学
  • 批准号:
    2309919
  • 财政年份:
    2023
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
Collaborative Research: Elements: A Cyberlaboratory for Randomized Numerical Linear Algebra
合作研究:Elements:随机数值线性代数网络实验室
  • 批准号:
    2309446
  • 财政年份:
    2023
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
Collaborative Research: Randomized Numerical Linear Algebra for Large Scale Inversion, Sparse Principal Component Analysis, and Applications
合作研究:大规模反演的随机数值线性代数、稀疏主成分分析及应用
  • 批准号:
    2152661
  • 财政年份:
    2022
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
Linear and nonlinear reduced models for the numerical approximation of high-dimensional functions
高维函数数值逼近的线性和非线性简化模型
  • 批准号:
    RGPIN-2021-04311
  • 财政年份:
    2022
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Discovery Grants Program - Individual
Collaborative Research: Randomized Numerical Linear Algebra for Large Scale Inversion, Sparse Principal Component Analysis, and Applications
合作研究:大规模反演的随机数值线性代数、稀疏主成分分析及应用
  • 批准号:
    2152704
  • 财政年份:
    2022
  • 资助金额:
    $ 43.24万
  • 项目类别:
    Standard Grant
Collaborative Research: Randomized Numerical Linear Algebra for Large Scale Inversion, Sparse Principal Component Analysis, and Applications
合作研究:大规模反演的随机数值线性代数、稀疏主成分分析及应用
  • 批准号:
    2152687
  • 财政年份:
    2022
  • 资助金额:
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  • 项目类别:
    Standard Grant
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