Regularization of Inverse ProblemsSpringer Science & Business Media, 31.07.1996 - 322 Seiten 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. |
Inhalt
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 |
299 | |
319 | |
Andere Ausgaben - Alle anzeigen
Regularization of Inverse Problems Heinz Werner Engl,Martin Hanke,A. Neubauer Eingeschränkte Leseprobe - 2000 |
Regularization of Inverse Problems Heinz Werner Engl,Martin Hanke,Günther Neubauer Keine Leseprobe verfügbar - 1996 |
Häufige Begriffe und Wortgruppen
Algorithm approximation approximation error assume bounded CGNE compact operator compute condition conjugate gradient conjugate gradient method consider continuous convergence rate convex corresponding data error defined definition denote discrepancy principle estimate Example finite-dimensional follows Fourier function hence Hilbert space holds ill-posed problems implies inequality integral equation inverse problems iterative methods L-curve Landweber iteration least-squares solution Lemma linear operator Math matrix maximum entropy minimizer Moore-Penrose generalized inverse nonlinear problems Note nullspace numerical obtain optimal order order-optimal orthogonal projector parameter choice rule proof of Theorem Proposition regularization method regularization parameter regularized solutions residual polynomials respect right-hand side Section selfadjoint semiiterative methods sequence singular value solving spectral family stopping rule subspace T¹y Tikhonov regularization unique v-method vector weakly yields zero θα
Beliebte Passagen
Seite 299 - Vogel. Analysis of bounded variation penalty methods for ill-posed problems.
Seite 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).
Seite 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.
Seite 299 - Problems 11 (1995), 639-653. [5] G. ALESSANDRINI, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172.