Stability of solution and reconstruction in inverse problems

本计画以应用科学中反问题之数学分析为基础，进行数学分析与数值分析，并从反问题的观点出发，探讨应用中的相关问题，准备可能的数值方法，取得令人满意的理论成果。此外，对于发展的数值方法的理论方面的基础上，已经提出了几种方法，并进行了测试的数值例子。我们还没有将数值结果与直接来自真实的世界（如工厂或工厂）的真实的数据进行比较。对于与反问题相关的问题的研究，参与者们根据各自的专业取得了显著的成果，我们多次组织国外学者进行反问题的调查，并参加反问题的国际会议，介绍本项目的成果。Yamamoto等人出版了一本关于反问题的数学和数值方法的专著。Onishi，Toyota，Iso，Kawarada，Miyoshi，Kimura，Ushijima和Kako从数值的角度研究了应用科学中的反问题和相关问题。中村、齐藤、池畑、田沼、久保等曾致力于反问题的理论研究。

This project aims at mathematical analysis and numerical analysis based on the mathematical analysis for inverse problems in applied sciences, Moreover we have studied related problems in applications, from the viewpoint of inverse problems, and prepared possible numerical methods.We conclude that by this project, we have established satisfactory theoretical results. Moreover, as for the development of numerical methods on the basis of the theoretical aspects, several methods have been proposed and tested for numerical examples. Still we have not compared the numerical results with real data directly from the real worlds such as works or plants. Therefore the continuation of this kind of projects are strongly demanded.For researches of related problems with inverse problems, the participants have achieved remarkable results by their own specialities.We have held several surveys concerning inverse problems by foreign researchers and taken part in international conferences on inverse problems for presenting the outputs of this project.With results obtained by this project, M. Yamamoto et al. have published a monograph on the mathematics and the numerical methods of inverse problems.Onishi, Tosaka, Iso, Kawarada, Miyoshi, Kimura, Ushijima and Kako have worked for inverse problems and related problems in applied sciences, from numerical points of view. Nakamura, Saitoh, Ikehata, Tanuma, Kubo have worked for theoretical aspects of inverse problems.