Development and Application of Ill-Posed Problems in the USSR

[+] Author and Article Information
Alexander Markovsky

AT&T, Bell Labs, Rm 3B-532, Crawfords Corner Rd, Holmdel, NJ 07733-1988

Appl. Mech. Rev 41(6), 247-256 (Jun 01, 1988) (10 pages) doi:10.1115/1.3151896 History: Online June 03, 2009


This article describes the earlier stage of development of ill-posed problems in the Soviet Union where this area of mathematics originated. There are several types of the problems, such as Fredholm and Volterra integral equations of the first kind, algebraic systems with ill-conditioned matrix, optimal regulations, approximate Fourier summation, inverse heat conduction, etc, where ill-posed nature is a serious barrier to construct a stable solution. Different methods, in increasing order of generality, showing how to interpret and solve these types of problems are reviewed. The main point is to demonstrate that all approaches in solving the ill-posed problems can be based on common sense and intuition, though formalization is needed to explore the methodology in different fields of applied mathematics and engineering.

Copyright © 1988 by American Society of Mechanical Engineers
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