Numerical Methods for the Solution of Ill-Posed Problems

✍ Scribed by A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola (auth.)

• Publisher: Springer Netherlands
• Year: 1995
• Tongue: English
• Leaves: 256
• Series: Mathematics and Its Applications 328
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-5
Regularization methods....Pages 7-63
Numerical methods for the approximate solution of ill-posed problems on compact sets....Pages 65-79
Algorithms for the approximate solution of ill-posed problems on special sets....Pages 81-96
Algorithms and programs for solving linear ill-posed problems....Pages 97-161
Back Matter....Pages 163-253

✦ Subjects

Computational Mathematics and Numerical Analysis; Integral Equations; Operator Theory; Optimization; Algorithms