Mathematical Sciences: Inverse Problems, Impedance Potentials, and Wavelets

这项研究涉及通过构造改进的势函数和小波的应用来实现反问题的高效和精确的数值解。在反问题中，人们试图根据关于其解的信息来重建方程，这导致了数值线性代数中的困难问题，因为对于大系统来说，重建必须在计算机上完成。这可能看起来很奇怪，但通常一个人在不确切知道问题本身是什么的情况下就有了解决问题的办法。想想你的医生在检查时给你照X光的例子，以找出是否有什么不对劲的地方。来自X光的数据本质上类似于解决方案，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ı方程式是什么特殊条件！正在生产Dataı解决方案！本着同样的精神，首席研究员将研究确定产生某些类型解的方程的数值技术。

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.