Numerical Methods for the Solution of Ill-Posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for the Solution of Ill-Posed Problems write by A.N. Tikhonov. This book was released on 2013-03-09. Numerical Methods for the Solution of Ill-Posed Problems available in PDF, EPUB and Kindle. 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.
Numerical Methods for Solving Inverse Problems of Mathematical Physics
Numerical Methods for Solving Inverse Problems of Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Methods for Solving Inverse Problems of Mathematical Physics write by A. A. Samarskii. This book was released on 2008-08-27. Numerical Methods for Solving Inverse Problems of Mathematical Physics available in PDF, EPUB and Kindle. The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.
Ill-Posed Problems: Theory and Applications
Ill-Posed Problems: Theory and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ill-Posed Problems: Theory and Applications write by A. Bakushinsky. This book was released on 2012-12-06. Ill-Posed Problems: Theory and Applications available in PDF, EPUB and Kindle. 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 modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques.
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Methods for Inverse Problems write by Curtis R. Vogel. This book was released on 2002-01-01. Computational Methods for Inverse Problems available in PDF, EPUB and Kindle. Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Iterative Methods for Ill-Posed Problems
Iterative Methods for Ill-Posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Iterative Methods for Ill-Posed Problems write by Anatoly B. Bakushinsky. This book was released on 2010-12-23. Iterative Methods for Ill-Posed Problems available in PDF, EPUB and Kindle. Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
