Regularization of Inverse Problems

Ön Kapak
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.

İçindekiler

II
3
III
4
IV
7
V
10
VI
12
VII
18
VIII
23
IX
25
XXXI
177
XXXII
181
XXXIII
186
XXXIV
191
XXXV
197
XXXVI
202
XXXVII
207
XXXVIII
210

X
31
XI
32
XII
36
XIII
42
XIV
49
XV
55
XVI
63
XVII
71
XVIII
80
XIX
83
XX
89
XXI
100
XXII
112
XXIII
117
XXIV
126
XXV
134
XXVI
140
XXVII
154
XXIX
160
XXX
166
XXXIX
215
XL
221
XLI
224
XLII
228
XLIII
233
XLIV
237
XLV
241
XLVI
243
XLVII
249
XLVIII
253
XLIX
256
L
262
LI
277
LII
285
LIII
289
LIV
291
LV
295
LVI
299
LVII
319
Telif Hakkı

Diğer baskılar - Tümünü görüntüle

Sık kullanılan terimler ve kelime öbekleri

Popüler pasajlar

Sayfa 299 - Vogel. Analysis of bounded variation penalty methods for ill-posed problems.
Sayfa 300 - Vessella, S.) Some inverse problems for a nonlinear parabolic equation connected with continuous casting of steel: Stability estimates and regularization. Numer. Funct. Anal. Optimization 11, No.7/8, 643-671 (1990).
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.
Sayfa 299 - Problems 11 (1995), 639-653. [5] G. ALESSANDRINI, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172.

Kaynakça bilgileri