An Introduction to the Mathematical Theory of Inverse Problems is popular PDF and ePub book, written by Andreas Kirsch in 1996-09-26, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, An Introduction to the Mathematical Theory of Inverse Problems can be Read Online from any device for your convenience.
An Introduction to the Mathematical Theory of Inverse Problems Book PDF Summary
Following Keller [119] we call two problems inverse to each other if the for mulation 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 ill-posed. It turns out that many interesting and important inverse in science lead to ill-posed problems, while the corresponding di problems rect 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.
Detail Book of An Introduction to the Mathematical Theory of Inverse Problems PDF
- Author : Andreas Kirsch
- Release : 26 September 1996
- Publisher : Springer Science & Business Media
- ISBN : 038794530X
- Genre : Science
- Total Page : 304 pages
- Language : English
- PDF File Size : 21,9 Mb
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