312.224 (23S) Selected Topics in Analysis: Discrete inverse problems

Sommersemester 2023

Registration deadline has expired.

First course session
02.03.2023 10:00 - 12:00 N.2.01 On Campus
... no further dates known

Overview

Lecturer
Course title german Selected Topics in Analysis: Discrete inverse problems
Type Lecture
Course model Attendance-based course
Hours per Week 2.0
ECTS credits 3.0
Registrations 9
Organisational unit
Language of instruction English
Course begins on 02.03.2023
eLearning Go to Moodle course

Time and place

List of events is loading...

Course Information

Intended learning outcomes

After successful completion of this course, students will know basic concepts and methods for discrete inverse problems. They will understand and will be able to prove the most important theoretical results and will be able to apply these methods to selected inverse problems.

Teaching methodology

Lecture

Course content

Discrete linear inverse problems deal with ill-conditioned systems of linear equations. This course focuses on the followings aspects:

  • Basic concepts for discrete inverse problems and examples
  • Least squares solutions and generalizations
  • Regularization methods for linear inverse problems
  • Inverse problems in imaging

Prior knowledge expected

Analysis 1-3. Numerics 1 would be a plus.

Literature

M. Richter, Inverse Problems: Basics, Theory and Applications in Geophysics (second edition), Birkhäuser,  2020

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

Examination methodology

Oral exam

Examination topic(s)

The contents of the lecture

Assessment criteria / Standards of assessment for examinations

Knowledge of definitions, methods and results.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
    • Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Compulsory subject)
      • Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
  • Bachelorstudium Technische Mathematik (SKZ: 201, Version: 17W.1)
    • Subject: Angewandte Analysis (Compulsory elective)
      • 8.5 Ausgewählte Kapitel der Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
          Absolvierung im 5., 6. Semester empfohlen
  • Bachelor's degree programme Technical Mathematics (SKZ: 201, Version: 22W.1)
    • Subject: Angewandte Analysis (Compulsory elective)
      • 8.5 Ausgewählte Kapitel der Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
  • Bachelor's degree programme Technical Mathematics (SKZ: 201, Version: 22W.1)
    • Subject: Angewandte Mathematik (Compulsory elective)
      • 11.1 Wahl von weiteren Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.9 Selected Topics in Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 22W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.7 Selected Topics in Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)
          Absolvierung im 1., 2., 3. Semester empfohlen
  • Doctoral programme Doctoral programme in Technical Sciences (SKZ: 786, Version: 12W.4)
    • Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums (Compulsory subject)
      • Studienleistungen gem. § 3 Abs. 2a des Curriculums ( 16.0h XX / 32.0 ECTS)
        • 312.224 Selected Topics in Analysis: Discrete inverse problems (2.0h VO / 3.0 ECTS)

Equivalent courses for counting the examination attempts

This course is not assigned to a sequence of equivalent courses