Optimal Methods for Ill-Posed Problems: With Applications to Heat Conduction

✍ Scribed by Vitalii P. Tanana; Anna I. Sidikova

• Publisher: De Gruyter
• Year: 2018
• Tongue: English
• Leaves: 138
• Series: Inverse and Ill-Posed Problems Series; 62
• Category: Library

✦ Synopsis

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics.

Contents
Modulus of continuity of the inverse operator and methods for solving ill-posed problems
Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind
Tikhonov regularization method
Projection-regularization method
Inverse heat exchange problems

• A compact and up-to-date overview of optimal methods for solving ill-posed problems
• Covers error estimates and applications to heat conduction problems
• Of interest to reseachers and graduate students in applied mathematics and engineering

✦ Table of Contents

Introduction
Contents
1. Modulus of continuity of the inverse operator and methods for solving ill-posed problems
2. Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind
3. Tikhonov regularization method
4. Projection-regularization method
5. Inverse heat exchange problems
References
Index