|
04906 Discrete Ill-Posed Problems
| |
Danish title: Discrete Ill-Posed Problems
| |
Language: English
Credit points: 5,1 |
|
| Type: | Ph.D.-level, Open University
Language: English |
| |
| |
| |
Compulsory: basic knowledge of numerical analysis
| |
| |
| |
Recommended semester: 7th - 9th semester
| |
Scope and form: lectures and exercises
| |
Examination: Evaluation of report(s) (Pass/fail)
| |
| |
| |
| |
| |
Department: Informatics and Mathematical Modelling
| |
Aim: The course describes the numerical treatment of inverse problems, with emphasis on various algorithms for computing stabilized solutions via incorporation of a priori information. The characteristics of inverse problems are discussed with emphasis on those aspects that influence their numerical splution. The inversion algorithms are described and compared in a commen framework, and their stable and efficient numerical implementation is discussed. The theory is illustrated with examples from e.g. seismology and signal processing.
| |
Contents: Introduction to inverese problems Discretization methods. Numerical linear algebra for discrete inverse problems; QR-factorization, singular value decomposition (SVD), and conjugate gradients (CG). Analysis of discrete ill-posed problems by means of the L-curve. Direct and iterative regularization methosd. Choice of smoothing norm and regularization parameter. Computer exercises using Matlab and the regularization tools toolbox Course plan: Day 1: Introduction, Singular value expansion. Day 2: Rank-dificient problems, SVD, GSVD. Day 3: Tikhonov regularization, Standard-form reduction. Day 4: Picard condition, L-curve analysis. Day 5: Seminorms, The TSVD family, Mollifier methods. Day 6: Parameter - choice methods. Day 7: Iterative methods.
|
|
|
