CompactCourse: Structured Matrices, Multigrid, and Image Processing - Summer14

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Term
Summer 14
Lecturer
Prof. Dr. Stefano Serra Capizzano, Como; contact: Univ.-Prof. Dr. Thomas Huckle
Time and Place
16:00-18:00 on June 20, room 10.3.11, June 23, 24, 25, 26, room 02.08.011 and 07.02.23, June 27. room 10.1.11
Audience
all interested students, in particular students of BGCE, TopMath, CSE, Mathematics, and Informatics
Tutorials
-
Exam
n.a.
Semesterwochenstunden / ECTS Credits
1 credits
TUMonline
TUMonline reference of lecture



News

Content

In the lecture, first mathematical properties of structured matrices are discussed. Especially matrix algebras like the class of circulant matrices are considered related to convolution and Discrete Fourier Transform. The derived properties can be used to introduce and analyse e.g. Fast Fourier Transform and multigrid methods. So a local Fourier analysis of multigrid methods can be based on this technique. Structured matrices problems arise in the solution of Partial Differential Equations (PDEs) and in image processing.

Preliminary Topics

  • Structured dense matrices: Applications. Spectral properties of Toeplitz matrices.
  • Band-preconditioning and spectral properties of the preconditioned matrices
  • Matrix algebras; matrix algebra preconditioning; classical Korovkin Theorem.
  • Korovkin theorem for matrix approximations. Pathologies of the multilevel case
  • Structured matrices and Multigrid methods
  • Structured matrices and image processing

Material

t.b.a.

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