Mathematical Sciences: Inverse Problems, Impedance Potentials, and Wavelets

数学科学：反问题、阻抗势和小波

• 批准号: 9006220
• 负责人: Gilbert Strang
• 金额: $ 19.35万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006220&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Inverse; Problems; Impedance

This research involves the efficient and accurate numerical solution of inverse problems by means of the construction of improved potential functions and the application of wavelets. In an inverse problem one tries to reconstruct an equation from information about its solutions, and this leads to difficult problems in numerical linear algebra, since for a large system the reconstruction must be done on a computer. It may seem strange but very often one has solutions to a problem without knowing exactly what the problem is itself. Think of the case where your doctor takes X-rays of you during an examination in order to find out if anything is amiss. The data from the X-rays are essentially like the solutions, whereas the problem in this case might be an unknown malady. Your doctor tries to determine what particular condition ıequation! is producing the data ısolutions!. In much the same spirit the principal investigator will study numerical techniques for determining the equations that are producing certain types of solutions.

这项研究涉及到有效和准确的数值 反问题的解决方法的建设 改进的势函数和小波的应用。 在反问题中，人们试图从 关于它的解决方案的信息，这导致了困难 数值线性代数中的问题，因为对于一个大系统， 必须在计算机上进行重建。 这可能看起来很奇怪，但通常一个人有解决方案， 不知道问题本身是什么。 想一想，你的医生在你生病的时候给你拍X光片。 检查一下，看看有没有什么不对劲。 数据 从X射线基本上是一样的解决方案，而 这种情况下的问题可能是一种未知的疾病。 你的医生 试图确定什么特定条件<$equation！是 生产数据解决方案！本着同样的精神， 首席研究员将研究数字技术， 确定产生某些类型的 解决方案