ILL-POSED PROBLEMS AND EXAMPLES OF INCORRECT PROBLEMS
Keywords:
ill-posed problems, well-posed problems, non-uniqueness of solutions, regularization, inverse problems, ill-conditioning, methods for solving ill-posed problems, practical applications, theoretical aspects, scientific research, applied fields (mathematics, physics, economics , IT), prevention of ill-posed problems.Abstract
This work examines the problem of ill-posed problems, which often arise in various fields of science and practice. Ill-posed problems are characterized by the lack of a unique solution, sensitivity to changes in input data, and instability of the solution. The aim of the work is to study the essence of ill-posed problems, identify the reasons for their occurrence, and consider examples from different areas of knowledge. Particular attention is paid to the theoretical aspects of ill-posed problems, such as non-uniqueness of the solution, sensitivity to input data, and uncertainty. The paper describes methods for solving ill-posed problems, including regularization, optimization, statistical, and machine learning methods. These approaches allow to deal with uncertainty and instability of the solution. The study of ill-posed problems is of great practical importance, as they often occur in real-life situations and require special methods for their solution.
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