| Type: | kursus på phd-niveau, udbydes under åben uddannelse
Sprog: engelsk |
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Obligatoriske forudsætninger: basic knowledge of numerical analysis
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Vejledende placering: Sidst i studiet.
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Undervisningsform: lectures and exercises
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Evalueringsform Rapportaflevering
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Karakter: bestået/ikke bestået
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Institut: Informatik og Matematisk Modellering
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Kursusmål: 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.
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Kursusindhold: 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.
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