Inverse and Ill-Posed Problems
2 primary works • 4 total works
Book 29
This monographis devoted tothe basic component of the theory of linear optimization problems: systems of linear inequalities. Such an approach is exact in both a historical and methodological sense.
In the first two chaptersdeal witheconomic interpretation of models, theorems and approaches. The other chapters are dedicated to less traditional problems of linear optimization, such as contradictory problems and duality, lexicographic problems and duality, piecewise linear problems and duality, and more. The bookalso covers some general methods for calculating processes for certain problems of linear optimization: the problem of stability and correctness.
In the first two chaptersdeal witheconomic interpretation of models, theorems and approaches. The other chapters are dedicated to less traditional problems of linear optimization, such as contradictory problems and duality, lexicographic problems and duality, piecewise linear problems and duality, and more. The bookalso covers some general methods for calculating processes for certain problems of linear optimization: the problem of stability and correctness.
Book 53
Operators and Iterative Processes of Fejer Type
by Vladimir V Vasin and Ivan I. Eremin
Published 1 January 2009
This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejer property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.
Theory of Linear Ill-Posed Problems and its Applications
by Valentin K. Ivanov, Vladimir V Vasin, and Vitalii P. Tanana
Published 1 January 2002
This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e.g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as well as in its applications. To reflect these accomplishments the authors included additional material e.g. comments to each chapter and a list of monographs with annotations.
Optimal Methods for Ill-Posed Problems
by Vitalii P. Tanana and Anna I. Sidikova
Published 19 March 2018
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics.
Contents
Modulus of continuity of the inverse operator and methods for solving ill-posed problems
Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind
Tikhonov regularization method
Projection-regularization method
Inverse heat exchange problems
Contents
Modulus of continuity of the inverse operator and methods for solving ill-posed problems
Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind
Tikhonov regularization method
Projection-regularization method
Inverse heat exchange problems