Last edited by Akinolar
Sunday, July 26, 2020 | History

3 edition of Inverse Problems (Advanced Lectures in Mathematics Series) found in the catalog.

Inverse Problems (Advanced Lectures in Mathematics Series)

Johan B. Baumeister

# Inverse Problems (Advanced Lectures in Mathematics Series)

## by Johan B. Baumeister

Written in English

Subjects:
• Mathematics,
• Mathematics (Specific Aspects)

• The Physical Object
FormatPaperback
ID Numbers
Open LibraryOL12768821M
ISBN 103528089652
ISBN 109783528089658
OCLC/WorldCa257908313

Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with Pages: Product Information. In the first, , edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes.

A Reading List in Inverse Problems Brian Borchers Draft of Janu This document is a bibliography of books, survey articles, and on-line doc-uments on various topics related to inverse problems. I’ve tried to avoid listing research papers, because there are far more research papers on each of these.   The first part of the book deals with discrete problems and describes Maximum likelihood, Monte Carlo, Least squares, and Least absolute values methods. The second part deals with inverse problems involving functions. The book is almost completely self-contained, with all important concepts carefully Edition: 1.

Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image.   The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions Author: Mathias Richter.

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The book, An Introduction to Inverse Problems with Applications, mentioned in Francisco Moura Neto's answer certainly appears both applied and gentle as an introduction. The main prerequisite seems to be linear algebra, but some exposure to multivariable calculus, numerical methods and differential equations would be valuable too.

The book is focussed on continuous eigenvalue, potential and scattering problems. For discrete inverse problems it is probably wiser to consider a different book.

This book helped me to understand the work of mathematicians such as Colton and Kress by: The forward problem corresponding to an inverse problem is usually a well defined problem in physics, engineering or medical imaging.

What is inverted in an inverse problem is the causality: Whereas in a forward problem we start from the causes and end up with the results, in an inverse problem we start with partial knowledge of the causes and. The book develops the statistical approach to inverse problems with an emphasis on modeling and computations.

The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability by: This book presents the theory of inverse spectral and scattering problems and of many other inverse Inverse Problems book for differential equations in an essentially self-contained way.

An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book. Inverse Problems book Inverse Problems Book Page.

This page contains the computational Matlab files related to the book Linear and Nonlinear Inverse Problems with Practical Applications written by Jennifer Mueller and Samuli Siltanen and published by SIAM in You can order the book at the SIAM webshop.

Using the codes requires some familiarity with the Matlab software. Classification of inverse problems. There are many kinds of inverse problems. For example, there are medium characterization problems, for which the goal is to obtain information about the IOPs of the medium, which in our case is the water body with all of its is the type of problem that we consider in this chapter.

Inverse Problem Theory: To download the book, click here (downloading, viewing, and printing allowed). To purchase the book from SIAM (85 $) click here. To purchase the book from Amazon (85$) click here.

Click here for the List of Errata. Recap: Characterising inverse problems Inverse problems can be continuous or discrete Continuous problems are often discretized by choosing a set of basis functions and projecting the continuous function on them.

The forward problem is to take a model and predict observables that are compared to actual data. Contains the Physics of the problem. Special Note: The above text lists for $75 but is available for a 10% discount if you indicate you saw it on the Inverse Problems WWW Page ; K. Kurpisz and A.J. Nowak, "Inverse Thermal Problems," Computational Mechanics Publishers, Boston, Alifanov, O. M., "Inverse Heat Transfer Problems", Springer Verlag, (ISBN or ISBN. The title of the book reflects this point of view: our insight about inverse problems must go hand-in-hand with our algorithms for solving these problems. Solving an inverse problem is rarely a matter of just picking an algorithm from a textbook, a research paper, or a software package. Publisher Summary. This chapter discusses a few geometrical features of inverse of problems. It presents the problems described by a mapping M of a set C called the set of parameters into a set E called the set of results. The solution of the inverse problem is either a true solution, when M(C) = E and the inverse mapping is sufficiently continuous for a reasonable distance in E, or a. Inverse problems can be found in many topics of engineering mechanics. There are many successful applications in the fields of inverse problems (non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc.). The inverse problems introduced in the previous chapters involve finding unknown functions (including functions defined on finite sets, that is, vectors or matrices) given other functions which Author: Charles Groetsch. This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist Author: Masahiro Yamamoto. About this Item: Springer US JunBuch. Condition: Neu. Neuware - Elucidates the fundamental mathematical structures of inverse problems, analyzing both the information content and the solution of some inverse problems in which the information content of the coefficients and the source term of a given differential equation is not too large. 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. This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the. The book highlights recent research focusing on reliable numerical techniques for the solution of inverse problems, with relevance to a range of fields including acoustics, electromagnetics, optics, medical imaging, and geophysics. Such problems are important in the identification of flying objects (airplanes, missiles etc.), objects immersed in water (submarines, fish), and in many other situations.\" \"This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. Problem Given any constants$a,b,c$where$a\neq 0$, find all values of$x$such that the matrix$A\$ is invertible if \[A= \begin{bmatrix} 1 & 0 & c \\. An inverse problem is a special kind of ill-posed problem that is particularly difficult to solve, and such problems are the subject of this book.

About the Author Mark Gockenbach received his PhD in Computational and Applied Mathematics from Rice University in Inverse problems of this type are often ill-posed in the sense that distinct causes can account for the same effect and small changes in a perceived effect can correspond to very large changes in a given cause.

Very frequently such inverse problems are modeled by .This category contains pages that are part of the On 2D Inverse Problems book. If a page of the book isn't showing here, please add text {{BookCat}} to the end of the page concerned.

You can view a list of all subpages under the book main page (not including the book main page itself), regardless of whether they're categorized, here.