### 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. 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.

Original language | English (US) |
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Pages (from-to) | 373-379 |

Number of pages | 7 |

Journal | IEEE Transactions on Antennas and Propagation |

Volume | 29 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1981 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Antennas and Propagation*,

*29*(2), 373-379. https://doi.org/10.1109/TAP.1981.1142573