Tikhonov / Goncharsky / Stepanov Numerical Methods for the Solution of Ill-Posed Problems

1995
ISBN: 978-94-015-8480-7
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 328, 253 Seiten, eBook

Reihe: Mathematics and Its Applications

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 constraints (non-negativity, monotonicity, convexity, etc.).
Besides the theoretical material, the book also contains a FORTRAN program library.
Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.

Zielgruppe

Research

Autoren/Hrsg.

Tikhonov, A.N.

Goncharsky, A.

Stepanov, V.V.

Yagola, Anatoly G.

Inhaltsverzeichnis

Preface to the English edition. Introduction. 1. Regularization methods. 2. Numerical methods for the approximate solution of ill-posed problems on compact sets. 3. Algorithms for the approximate solution of ill-posed problems on special sets. 4. Algorithms and programs for solving linear ill-posed problems. Appendix: Program listings. Postscript. Index.