逆问题数学理论导论 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024


逆问题数学理论导论

简体网页||繁体网页
A.Kirsch 作者
世界图书出版公司
译者
1999-10 出版日期
278 页数
42.00元 价格
丛书系列
9787506242516 图书编码

逆问题数学理论导论 在线电子书 图书标签: 数学   


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发表于2024-12-23


逆问题数学理论导论 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

逆问题数学理论导论 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

逆问题数学理论导论 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024



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Following Keller [119] we call two problems inverse to each other if the formulation of each of them requires full or partial knowledge of the other. By this definition, it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually, one of the problems has been studied earlier and, perhaps, in more detail. This one is usually called the direct problem, whereas the other is the inverse problem. However, there is often another, more important difference between these two problems. Hadamard (see [91]) introduced the concept of a well-posed problem, originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness, existence, and stability of the solution. If one of the properties fails to hold, he called the problem iU-posed. It turns out that many interesting and important inverse problems in science lead to ill-posed problems,, while the corresponding direct problems are well-posed. Often, existence and uniqueness can be forced by enlarging or reducing the solution space (the space of "models"). For restoring stability, however, one has to change the topology of the spaces,which is in many cases impossible because of the presence of measurement errors. At first glance, it seems to be impossible to compute the solution of a problem numerically if the solution of the problem does not depend continuously on the data, i.e., for the case of ill-posed problems. Under additional a priori information about the solution, such as smoothness and bounds on the derivatives, however, it is possible to restore stability and construct efficient numerical algorithms.

  本书为英文版。

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