Well-Posed Linear Systems - 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 Well-Posed Linear Systems write by Olof J. Staffans. This book was released on 2005-02-24. Well-Posed Linear Systems available in PDF, EPUB and Kindle. Publisher Description
Well-Posed Linear Systems
Well-Posed Linear Systems - 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 Well-Posed Linear Systems write by Olof Staffans. This book was released on 2005-02-24. Well-Posed Linear Systems available in PDF, EPUB and Kindle. Many infinite-dimensional linear systems can be modelled in a Hilbert space setting. Others, such as those dealing with heat transfer or population dynamics, need to be set more generally in Banach spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting. It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be extended to these more general classes of systems, and complements them with new results which have no finite-dimensional counterpart. Much of the material presented is original, and many results have never appeared in book form before. A comprehensive bibliography rounds off this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.
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.
Well-posed, Ill-posed, and Intermediate Problems with Applications
Well-posed, Ill-posed, and Intermediate Problems with 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 Well-posed, Ill-posed, and Intermediate Problems with Applications write by Petrov Yuri P.. This book was released on 2011-12-22. Well-posed, Ill-posed, and Intermediate Problems with Applications available in PDF, EPUB and Kindle. This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Numerical Methods for the Solution of Ill-Posed Problems
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.
