Computational Methods for Inverse Problems

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 m

This book focuses on finding all ordinary differential equations that satisfy a given set of properties, thus dedicating itself to inverse problems of ordinary differential equations. The Nambu bracke

Computational and Statistical Methods for Analysing Big Data with Applications begins with an overview of the era of big data. It then goes on to explain different computational and statistical method

Adopting a novel approach to the topic by combining theoretical knowledge and practical results, this book presents the most popular and useful computational and experimental methods applied for study

This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hype

This book offers unique insight on structural safety and reliability by combining computational methods that address multiphysics problems, involving multiple equations describing different physical p

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research—including the authors’ own substantial projects—on uncertainty propagation and quantification. It covers two sourc

In Methods in Latin Computational Linguistics, Barbara McGillivray presents some of the methodological foundations of Latin Computational Linguistics through three corpus case studies covering morpho-

Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasi

Novel physical solutions, including new results in the field of adaptive methods and inventive approaches to inverse problems, original concepts based on high harmonic imaging algorithms, intriguing v

Computational Fluid-Structure Interaction: Methods and Applications takes the reader from the fundamentals of computational fluid and solid mechanics to the state-of-the-art in computational FSI metho

Based on a lecture course he taught for 15 years, Kukudzhanov (Ishlinsky Institute for Problems in Mechanics, Russia) introduces computational methods in continuum thermomechanics. He covers basic equ

Computational aeroacoustics (CAA) is a relatively new research area. CAA algorithms have developed rapidly and the methods have been applied in many areas of aeroacoustics. The objective of CAA is not simply to develop computational methods but also to use these methods to solve practical aeroacoustics problems and to perform numerical simulation of aeroacoustic phenomena. By analysing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. This is both a textbook for graduate students and a reference for researchers in CAA and as such is self-contained. No prior knowledge of numerical methods for solving partial differential equations (PDEs) is needed, however, a general understanding of partial differential equations and basic numerical analysis is assumed. Exercises are included and are designed to be an integral part of the chapter content. In addition, sample computer programs are included to illustrate the implementation of

Mechanical engineers mostly from Portugal and India, but also Greece and Japan, describe their research and report its findings on computational methods for optimizing manufacturing equipment and proc

Computational methods have become an indispensible tool for elucidating the mechanism of organometallic reactions. This snapshot of state-of-the-art computational studies provides an overview of the v

This second edition presents the theory of continuum mechanics using computational methods. The text covers a broad range of topics including general problems of large rotation and large deformations and the development and limitations of finite element formulations in solving such problems. Dr Shabana introduces theories on motion kinematics, strain, forces and stresses and goes on to discuss linear and nonlinear constitutive equations, including viscoelastic and plastic constitutive models. General nonlinear continuum mechanics theory is used to develop small and large finite element formulations which correctly describe rigid body motion for use in engineering applications. This second edition features a new chapter that focuses on computational geometry and finite element analysis. This book is ideal for graduate and undergraduate students, professionals and researchers who are interested in continuum mechanics.

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

Revised and?updated, this second edition of Walter Gautschi's successful Numerical Analysis?explores?computational methods?for problems arising in the areas of classical analysis, approximation theory

This book constitutes the thoroughly refereed post-proceedings of the 7th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, CIBB 2010, held in Palermo,

This volume contains the results of the workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, held in Karlsruhe, Germany, and represents a balanced selection o

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second

The current rapid and complex advancement applications of electromagnetic (EM) and optical systems calls for a much needed update on the computational methods currently in use. Completely revised and

Computational Methods for the Innovative Design of Electrical Devices isentirely focused on the optimal design of various classes of electrical devices. Emerging new methods, like e.g. those based on

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

Recent computational and modeling advances have produced methods for estimating species trees directly, avoiding the problems and limitations of the traditional phylogenetic paradigm where an estimat

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined

This handbook offers guidance on selections of appropriate computational methods and software packages for specific genetic problems. Coverage strikes a balance between methodological expositions and

Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems.

Model Building is the most fruitful area of economics, designed to solve real-world problems using all available methods such as mathematical, computational and analytical, without distinction. Wherev

The subject of computational plasticity encapsulates the numerical methods used for the finite element simulation of the behaviour of a wide range of engineering materials considered to be plastic &#

Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter

The advent of high-speed computers has encouraged a growing demand for newly graduated engineers to possess the basic skills of computational methods for heat and mass transfer and fluid dynamics. Com

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Eart

The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book, first published in 2005, offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes and constructing phylogenies. The first part of this book consists of four chapters on the themes of Statistics, Computation, Algebra and Biology, offering speedy, self-contained introductions to the emerging field of algebraic statistics and its applications to genomics. In the second part, the four themes are combined and developed to tackle real problems in computational genomics. As the first book in the exciting and dynamic area, it wi

Here is a book for anyone who would like to become better acquainted with the modern tools of numerical analysis for several significant computational problems arising in finance. The authors review s

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

The critical role of trace gases in global atmospheric change makes an improved understanding of these gases imperative. Measurements of the distributions of these gases in space and time provide important information, but the interpretation of this information often involves ill-conditioned model inversions. A variety of techniques have therefore been developed to analyze these problems. Inverse Problems in Atmospheric Constituent Transport is the first book to give comprehensive coverage of work on this topic. The trace gas inversion problem is presented in general terms and the various different approaches are unified by treating the inversion problem as one of statistical estimation. Later chapters demonstrate the application of these methods to studies of carbon dioxide, methane, halocarbons and other gases implicated in global climate change. This book is aimed at graduate students and researchers embarking upon studies of global atmospheric change, biogeochemical cycles and Eart

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for thr

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astrono