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Relevant bibliographies by topics / Inverse Problems (Mathematics)

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Dissertations / Theses

Academic literature on the topic 'Inverse Problems (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Dissertations / Theses on the topic "Inverse Problems (Mathematics)"

1

Agapiou, Sergios. "Aspects of Bayesian inverse problems." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/60138/.

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The goal of this thesis is to contribute to the formulation and understanding of the Bayesian approach to inverse problems in function space. To this end we examine two important aspects of this approach: the frequentist asymptotic properties of the posterior, and the extraction of information from the posterior via sampling. We work in a separable Hilbert space setting and consider Gaussian priors on the unknown in conjugate Gaussian models. In the first part of this work we consider linear inverse problems with Gaussian additive noise and study the contraction in the small noise limit of the

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2

Wokiyi, Dennis. "Non-linear inverse geothermal problems." Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143031.

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The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that i

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3

Klimmek, Martin. "On inverse problems in mathematical finance." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55821/.

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We consider two inverse problems motivated by questions in mathematical finance. In the first two chapters (Part 1) we recover processes consistent with given perpetual American option prices. In the third and fourth chapters (Part 2) we construct model-independent bounds for prices of contracts based on the realized variance of an asset price process. The two parts are linked by the question of how to recover information about asset price dynamics from option prices: in part one we assume knowledge of perpetual American option prices while in the second part we will assume knowledge of Europe

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4

Attalla, Atia May Ramsis. "Inverse eigenvalue problems : theory and algorithms." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299725.

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5

Cheang, Ka Hang. "Two problems on inverse eigenvalue problems and Hadamard finite part integrals." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182891.

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6

Chada, Neil Kumar. "Ensemble based methods for geometric inverse problems." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/111386/.

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Since the development of the ensemble Kalman filter, it has seen a wide application to many scientific fields ranging from signal processing to weather forecasting and reservoir simulation. One field which has recently seen a keen interest towards filtering techniques is that of inverse problems. Ensemble-based methods are a popular choice of filtering techniques as they provide a computational advantage over traditional methods whilst retaining a good level of accuracy. This thesis is concerned with developing analysis and numerics of ensemble Kalman inversion (EKI) in the context of Bayesian

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7

Dunlop, Matthew M. "Analysis and computation for Bayesian inverse problems." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/86136/.

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Many inverse problems involve the estimation of a high dimensional quantity, such as a function, from noisy indirect measurements. These problems have received much study from both classical and statistical directions, with each approach having its own advantages and disadvantages. In this thesis we focus on the Bayesian approach, in which all uncertainty is modelled probabilistically. Recently the Bayesian approach to inversion has been developed in function space. Much of the existing work in the area has been focused on the case when the prior distribution produces samples which are continu

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8

Tian, Na. "Novel optimisation methods for numerical inverse problems." Thesis, University of Greenwich, 2011. http://gala.gre.ac.uk/9099/.

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Inverse problems involve the determination of one or more unknown quantities usually appearing in the mathematical formulation of a physical problem. These unknown quantities may be boundary heat flux, various source terms, thermal and material properties, boundary shape and size. Solving inverse problems requires additional information through in-situ data measurements of the field variables of the physical problems. These problems are also ill-posed because the solution itself is sensitive to random errors in the measured input data. Regularisation techniques are usually used in order to dea

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9

Zhong, Ming. "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." Thesis, University of Maryland, College Park, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128674.

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<p> We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedne

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10

Kempton, Mark Condie. "The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2182.

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For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

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