Inverse Probleme Mit Stochastisch Modellierten Messdaten
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Inverse Probleme Mit Stochastisch Modellierten Messdaten

Inverse Probleme Mit Stochastisch Modellierten Messdaten


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About the Book

Wesentliche Zielsetzung dieses Buchs ist eine in sich abgeschlossene Darstellung der zur Lösung inverser Probleme notwendigen Kenntnisse von der mathematischen Analyse bis zur numerischen Lösung. Konkrete Anwendungsfälle aus Naturwissenschaften und Technik geben den Umfang der benötigten mathematischen Methoden vor. Dazu gehört insbesondere die stochastische Modellierung der unvorhersehbaren Störungen von Messdaten, die bisher in Lehrbüchern zu inversen und schlecht gestellten Problemen nicht berücksichtigt wird. Die stochastische Modellierung steht in engem Zusammenhang mit der für den Computereinsatz essentiellen Diskretisierung beziehungsweise Parametrisierung inverser Probleme, auf die besonderes Augenmerk gerichtet wird. Ein weiterer Schwerpunkt ist die praktische Lösung der aus der Diskretisierung resultierenden globalen, im Allgemeinen nichtlinearen Optimierungsprobleme. Hingegen wird auf die Besprechung einer abstrakten Theorie der Regularisierung verzichtet.

Um den ganzen Weg von der theoretischen Analyse bis zur effizienten numerischen Lösung inverser Probleme aufzeigen zu können, wird die Besprechung mathematischer Grundlagen gegenüber Standardtexten um die Einbeziehung von Themen der Wahrscheinlichkeitstheorie und Statistik, der Approximation mit Wavelets und dünnen Gittern sowie der globalen Optimierung wesentlich erweitert.

Für eine Reihe von repräsentativen Anwendungsfällen aus den Bereichen Mobilfunk, Medizintechnik oder Geophysik werden die jeweiligen, zumeist nichtlinearen Probleme mathematisch präzisiert, eingehend analysiert und rechnerisch gelöst.

Das Buch ist zum Selbststudium für Mathematiker und für mathematisch interessierte Ingenieure und Naturwissenschaftler geeignet.
About the Author: Univ.-Prof. Dr. Mathias Richter, Studium Mathematik TU München 1985-1990, Promotion in Mathematik 1996 an der TU München bei Prof. Dr. C. Reinsch, 1996-2010 Research Scientist bei Siemens, seit 2010 Professor für Mathematik an der Universität der Bundeswehr München, Fakultät für Elektrotechnik und Informationstechnik.

Univ.-Prof. Dr. Dr. Stefan Schäffler, Studium Mathematik TU München 1981-1986, Promotion Mathematik 1988, Habilitation Mathematik 1995, Promotion Elektrotechnik und Informationstechnik 1997 (alles TU München), 1997-2000 Senior Principal Research Scientist bei der SIEMENS AG (1998-2000 in Teilzeit), 1998-2000 Professor für Angewandte Mathematik (C3) in Erlangen, seit Dez. 2000 Universität der Bundeswehr München, Fakultät für Elektrotechnik und Informationstechnik, Professur für Mathematik und Operations Research.


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Product Details
  • ISBN-13: 9783662663424
  • Publisher: Springer
  • Publisher Imprint: Springer Spektrum
  • Height: 234 mm
  • No of Pages: 289
  • Spine Width: 17 mm
  • Weight: 485 gr
  • ISBN-10: 3662663422
  • Publisher Date: 01 Dec 2022
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Sub Title: Stochastische Und Numerische Methoden Der Diskretisierung Und Optimierung
  • Width: 156 mm


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