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Bücher Englische Bücher An Introduction to the Mathematical Theory of Inverse Problems
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An Introduction to the Mathematical Theory of Inverse Problems
Andreas Kirsch (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
12.10.2011
Sprache
Englisch
EAN
9781461253402
Herausgeber
Springer US
Serien- oder Bandtitel
Applied Mathematical Sciences
Sonderedition
Nein
Autor
Andreas Kirsch
Seitenanzahl
300
Einbandart
Broschiert
Bandzählung
120
Schlagwörter
CON_D029
Thema-Inhalt
GPFC - Kybernetik und Systemtheorie
PBKQ - Variationsrechnung
PBU - Optimierung
PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.5 cm
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