Regularization of Inverse Problems
Springer Science & Business Media, 31 Tem 1996 - 322 sayfa
In the last two decades, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics. This growth has largely been driven by the needs of applications both in other sciences and in industry. In Chapter 1, we will give a short overview over some classes of inverse problems of practical interest. Like everything in this book, this overview is far from being complete and quite subjective. As will be shown, inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e., to ill-posed problems. This means especially that their solution is unstable under data perturbations. Numerical meth ods that can cope with this problem are the so-called regularization methods. This book is devoted to the mathematical theory of regularization methods. For linear problems, this theory can be considered to be relatively complete and will be de scribed in Chapters 2 - 8. For nonlinear problems, the theory is so far developed to a much lesser extent. We give an account of some of the currently available results, as far as they might be of lasting value, in Chapters 10 and 11. Although the main emphasis of the book is on a functional analytic treatment in the context of operator equations, we include, for linear problems, also some information on numerical aspects in Chapter 9.
Kullanıcılar ne diyor? - Eleştiri yazın
Her zamanki yerlerde hiçbir eleştiri bulamadık.
Diğer baskılar - Tümünü görüntüle
a-priori additional Algorithm applied approximation assertion assume assumptions bounded called Chapter choose closed compact compute condition Consequently consider continuous convergence rate convex corresponding defined definition denote depends derivative determine discrepancy principle element equation equivalent error estimate exact Example exists fact fixed follows function further give given hand hence holds ill-posed implies inequality integral inverse problems iteration Landweber iteration leads Lemma linear matrix means measure minimizer Moreover namely noise nonlinear norm Note obtain operator optimal orthogonal parameter choice rule positive possible Proof properties Proposition prove regularization method regularization parameter Remark replaced respect restriction right-hand side satisfies seen sense sequence shown smoothness solution solving space spectral stopping sufficiently term Theorem Tikhonov regularization transform turn unique weakly yields zero
Sayfa 299 - Vogel. Analysis of bounded variation penalty methods for ill-posed problems.
Sayfa 310 - Inverse problems related to the mechanics and fracture of solids and structures", JSME Int.
Sayfa 300 - AB Bakushinskii, The problem of the convergence of the iteratively regularized Gauss-Newton method, Comput. Math. Math. Phys. 32, 1353-1359 (1992) [BB01] T.