Operator-theoretic and computational approaches to ill-posed problems with applications to antenna theory
Abstract
A general framework is developed for regularization and approximation methods concerned with ill-posed problems in which three levels in the resolution processes are distinguished and emphasized: (1) philosophy of resolution, (2) regularization-approximation schema, and (3) regularization algorithms. Dilemmas and methodologies of resolution of ill-posed problems and their numerical implementation are examined in this framework with particular reference to the problem of finding numerically minimum weighted-norm, least-squares solutions of first-kind integral equations. Emphasis is placed on the role of constraints, function space methods, the role of generalized inverses, and reproducing kernels in the regularization and stable computational resolution of these problems. Although the results are applied specifically to the problems of antenna synthesis and identification, the paper focuses on operator-theoretic and numerical methods.
- Publication:
-
IEEE Transactions on Antennas and Propagation
- Pub Date:
- March 1981
- DOI:
- 10.1109/TAP.1981.1142564
- Bibcode:
- 1981ITAP...29..220N
- Keywords:
-
- Antenna Design;
- Antenna Radiation Patterns;
- Approximation;
- Function Space;
- Functional Analysis;
- Optimization;
- Algorithms;
- Far Fields;
- Hilbert Space;
- Kernel Functions;
- Least Squares Method;
- Numerical Analysis;
- Communications and Radar