Some Mathematical Considerations in Dealing with the Inverse Problem.
Abstract
Many problems of mathematical physics can be formulated in terms of the operator equation Ax = y, where A is an integro-differential operator. Given A and x, the solution for y is usually straightforward. However, the inverse problem which consists of the solution for x when given A and y, is much more difficult. In this paper the following questions relative to the inverse problem are explored: (1) Does specification of the operator A determine the set (y) for which a solution x is possible? (2) Does the inverse problem always have a unique solution? (3) Do small perturbations of the forcing function y always result in small perturbations of the solution? (4) What are some of the considerations that enter into the choice of a solution technique for a specific problem? The concept of an ill-posed problem versus that of a well-posed problem is discussed. Specifically, the manner by which an ill-posed problem may be regularized to a well-posed problem is presented. The concepts are illustrated by several examples. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1980
- Accession Number
- ADA092261
Entities
People
- Donald D. Weiner
- Tapan K. Sarkar
- Vijay K. Jain
Organizations
- Rochester Institute of Technology