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Fast Transforms for Gaussian Random Fields
Fast Transforms for Gaussian Random Fields
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103539
- ISBN
- 9798293886845
- DDC
- 519
- 저자명
- Beckman, Paul G.
- 서명/저자
- Fast Transforms for Gaussian Random Fields
- 발행사항
- [Sl] : New York University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 125 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: O'Neil, Michael.
- 학위논문주기
- Thesis (Ph.D.)--New York University, 2025.
- 초록/해제
- 요약The spectral properties of functions and operators provide key insights into their structure, and form the basis for state-of-the-art computational methods for simulation, learning, and inference. By providing a fast transform between physical and frequency spaces, the fast Fourier transform revolutionized applications across computational mathematics. However, there remain many settings in which spectral methods cannot be efficiently applied because the geometric or analytic structure of the problem is not directly amenable to the fast Fourier transform. Motivated by parameter estimation and sampling problems in spatial statistics and uncertainty quantification, we develop numerical methods in three such settings.First, we discuss an adaptive integration method for computing continuous Fourier transforms of singular functions which is accelerated by existing nonuniform fast Fourier transform algorithms. Next, we develop a nonuniform fast Hankel transform for computing Fourier transforms of radially symmetric functions in higher dimensions. Finally, we present a manifold harmonic transform for performing Fourier analysis on arbitrary smooth manifolds by leveraging a multilevel low-rank approximation known as a butterfly factorization. In each case, we show how these fast transforms yield scalable methods for Gaussian random fields, and we briefly comment on other applications including imaging, graphics, and numerical partial differential equations.
- 일반주제명
- Applied mathematics
- 일반주제명
- Computer science
- 일반주제명
- Statistics
- 기타저자
- New York University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798293886845
■035 ▼a(MiAaPQ)AAI32040795
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aBeckman, Paul G.
■24510▼aFast Transforms for Gaussian Random Fields
■260 ▼a[Sl]▼bNew York University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a125 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: O'Neil, Michael.
■5021 ▼aThesis (Ph.D.)--New York University, 2025.
■520 ▼aThe spectral properties of functions and operators provide key insights into their structure, and form the basis for state-of-the-art computational methods for simulation, learning, and inference. By providing a fast transform between physical and frequency spaces, the fast Fourier transform revolutionized applications across computational mathematics. However, there remain many settings in which spectral methods cannot be efficiently applied because the geometric or analytic structure of the problem is not directly amenable to the fast Fourier transform. Motivated by parameter estimation and sampling problems in spatial statistics and uncertainty quantification, we develop numerical methods in three such settings.First, we discuss an adaptive integration method for computing continuous Fourier transforms of singular functions which is accelerated by existing nonuniform fast Fourier transform algorithms. Next, we develop a nonuniform fast Hankel transform for computing Fourier transforms of radially symmetric functions in higher dimensions. Finally, we present a manifold harmonic transform for performing Fourier analysis on arbitrary smooth manifolds by leveraging a multilevel low-rank approximation known as a butterfly factorization. In each case, we show how these fast transforms yield scalable methods for Gaussian random fields, and we briefly comment on other applications including imaging, graphics, and numerical partial differential equations.
■590 ▼aSchool code: 0146.
■650 4▼aApplied mathematics
■650 4▼aComputer science
■650 4▼aStatistics
■653 ▼aApplied harmonic analysis
■653 ▼aComputational statistics
■653 ▼aGaussian random fields
■653 ▼aIntegral operators
■653 ▼aNumerical analysis
■690 ▼a0364
■690 ▼a0984
■690 ▼a0463
■71020▼aNew York University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0146
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357635▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
