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Numerical Methods for the Solution of Ill-Posed Problems
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Equations of Mathematical Physics
Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathem...
nonlinear analysis and applications
This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.
Pseudosolution of Linear Functional Equations
In the book there are introduced models and methods of construction of pseudo-solutions for the well-posed and ill-posed linear functional equations circumscribing models passive, active and complicated experiments. Two types of the functional equations are considered: systems of the linear algebraic equations and linear integral equations. Methods of construction of pseudos6lutions are developed in the presence of passive right-hand side errors for two types of operator errors: passive measurements and active representation errors of the operator, and all their combinations. For the determined and stochastic models of passive experiments the method of the least distances of construction of ...
Inverse Problems: Tikhonov Theory And Algorithms
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 computati...
Ill-Posed Problems: Theory and Applications
Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill posed problems in...
An Introduction to the Mathematical Theory of Inverse Problems
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to e...
Gravity Inversion and Integration
This book contains theory and applications of gravity both for physical geodesy and geophysics. It identifies classical and modern topics for studying the Earth. Worked-out examples illustrate basic but important concepts of the Earth’s gravity field. In addition, coverage details the Geodetic Reference System 1980, a versatile tool in most applications of gravity data. The authors first introduce the necessary mathematics. They then review classic physical geodesy, including its integral formulas, height systems and their determinations. The next chapter presents modern physical geodesy starting with the original concepts of M.S. Molodensky. A major part of this chapter is a variety of mo...
Inverse Engineering Handbook
Inverse problems have been the focus of a growing number of research efforts over the last 40 years-and rightly so. The ability to determine a "cause" from an observed "effect" is a powerful one. Researchers now have at their disposal a variety of techniques for solving inverse problems, techniques that go well beyond those useful for relatively si
Numerical Methods of Solving Ill-posed Problems of Dielectric Spectrometry
Numerical Methods of Solving Ill-Posed Problems of Dielectric Spectrometry
