Inverse Problems Tikhonov Theory And Algorithms PDF Download
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Author | : Ito Kazufumi |
Publisher | : World Scientific |
Total Pages | : 332 |
Release | : 2014-08-28 |
Genre | : Mathematics |
ISBN | : 9814596213 |
Download Inverse Problems: Tikhonov Theory And Algorithms Book in PDF, ePub and Kindle
Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.
Author | : Kazufumi Ito |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 319 |
Release | : 2014-07 |
Genre | : Mathematics |
ISBN | : 9789814596190 |
Download Inverse Problems Book in PDF, ePub and Kindle
Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems. It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.
Author | : Per Christian Hansen |
Publisher | : SIAM |
Total Pages | : 220 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 089871883X |
Download Discrete Inverse Problems Book in PDF, ePub and Kindle
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
Author | : Curtis R. Vogel |
Publisher | : SIAM |
Total Pages | : 195 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 0898717574 |
Download Computational Methods for Inverse Problems Book in PDF, ePub and Kindle
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Author | : Martin Hanke |
Publisher | : SIAM |
Total Pages | : 171 |
Release | : 2017-01-01 |
Genre | : Mathematics |
ISBN | : 1611974933 |
Download A Taste of Inverse Problems Book in PDF, ePub and Kindle
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. A Taste of Inverse Problems: Basic Theory and Examples?presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. This book rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations; presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.
Author | : Richard C. Aster |
Publisher | : Elsevier |
Total Pages | : 404 |
Release | : 2018-10-16 |
Genre | : Science |
ISBN | : 0128134232 |
Download Parameter Estimation and Inverse Problems Book in PDF, ePub and Kindle
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner
Author | : Mikhail M. Lavrent'ev |
Publisher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2012-05-07 |
Genre | : Mathematics |
ISBN | : 3110915529 |
Download Inverse Problems of Mathematical Physics Book in PDF, ePub and Kindle
This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Author | : Larisa Beilina |
Publisher | : Springer Nature |
Total Pages | : 147 |
Release | : 2020-06-30 |
Genre | : Mathematics |
ISBN | : 3030486346 |
Download Mathematical and Numerical Approaches for Multi-Wave Inverse Problems Book in PDF, ePub and Kindle
This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.
Author | : Alemdar Hasanov Hasanoğlu |
Publisher | : Springer Nature |
Total Pages | : 521 |
Release | : 2021-08-02 |
Genre | : Mathematics |
ISBN | : 303079427X |
Download Introduction to Inverse Problems for Differential Equations Book in PDF, ePub and Kindle
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.
Author | : Otmar Scherzer |
Publisher | : Springer Science & Business Media |
Total Pages | : 1626 |
Release | : 2010-11-23 |
Genre | : Mathematics |
ISBN | : 0387929193 |
Download Handbook of Mathematical Methods in Imaging Book in PDF, ePub and Kindle
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.