Numerical Algorithm for Inverse Problems and its Visualization.

反问题的数值算法及其可视化。

• 批准号: 06650071
• 负责人: KITAGAWA Takashi
• 金额: $ 1.28万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06650071/
• 关键词: Inverse Problems; Regularization Method; III-Posed Problems; Numerical Algorithms; 可視化システム; 不安定性

In this research project, we designed and analyzed numerical algorithm for inverse problems. The problems originally comes from inversion of compact operators whose typical example is Fredholm integral equations of the first kind. Our main theme includes developing stable numerical algorithm and giving its mathematical foundations. Moreover we extended our algorithms to multimedia information system and proposed new mathematical model which enables semantic interpretation of data items.The essential operation of regularization is that selecting an appropriate subspace according to the constraint. In the case of the integral equation the constraint is the smoothness of the solution. We generalized this operation to semantic interpretation where the constraint corresponds to context. We can deal with meaning which is the relation of content and the context using the model. This model is applied to actual information systems including meta-database systems and associative search for multimedia data.

在本研究计画中，我们设计并分析反问题的数值演算法。这些问题最初来自紧算子的反演，其典型例子是第一类Fredholm积分方程。我们的主题包括发展稳定的数值算法，并给出其数学基础。此外，我们还将算法推广到多媒体信息系统中，提出了新的数学模型，使数据项能够进行语义解释，正则化的基本操作是根据约束条件选择合适的子空间。在积分方程的情况下，约束是解的光滑性。我们将此操作推广到语义解释，其中约束对应于上下文。我们可以用这个模型来处理意义，即内容和语境的关系。这个模型被应用到实际的信息系统，包括元数据库系统和多媒体数据的关联搜索。

项目成果

T.Kitagawa :"A method for examining stability of a class of numerical procedures," Proceeding of HERMIS'94. 81-88 (1995)

T.Kitakawa：“一种检查一类数值过程稳定性的方法”，HERMIS94 论文集。

Y.Kiyoki and T.Kitagawa: "A fundamental framework for realizing semantic interoperability," Integrated Computer-Aided Enginering. 2. 3-20 (1995)

Y.Kiyoki 和 T.Kitakawa：“实现语义互操作性的基本框架”，集成计算机辅助工程。

T.Kitagawa: "A method for eramining stability of aclass of hururial procedures" Proceedings of HERMIS′94. 81-88 (1995)

T. Kitakawa：“一种消除一类 hururial 程序稳定性的方法”，HERMIS94 论文集（1995 年）。

Y. Kiyoki & T. Kitagawa: "Asemantic assoucative search method for kuowledgc Aguisition" Inforvation Modelling and Knowledgc Baces. 6. 121-130 (1995)

Y·清木

T.Kitagawa: "A method for examining stability of a class of numerical procedures" Proceeding of HERMIS'94. 81-88 (1995)

T.Kitakawa：“一种检查一类数值过程稳定性的方法”HERMIS94 论文集。