Fundamental Concepts in Inverse Problems
The final answer to several problems can be reduced to evaluating a function–the solution function or the solution operator–and in the case of inverse problems it is not different. This is the point of view of a mathematician – insisting in the use of the notion of function. Not that one can always come about with the solution operator explicitly, but we can think abstractly on it and deduce its properties. This justifies the treatment that we present in this chapter of some of the aspects and complications that arise in the evaluation of functions. Next, we discuss some general aspects of mathematical models and inverse problems. A few classification schemes of inverse problems, illuminating different aspects, are presented. These classifications are used in subsequent chapters.
KeywordsInverse Problem Absolute Error Multiplication Factor Condition Number Fundamental Concept
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