Structured matrices, like Toeplitz matrices or circulant matrices, arise in many applications, including image processing or in scientific computing in general. Besides the existance of fast algorithsm for matrix multiplication and in many cases even inversion, the presence of structure also allows for a detailed analysis of advanced numerical methods. Further, the presence of structure can be exploited for extremely efficient implementations on modern computer architectures, resulting in extremely fast methods overall.
In this course structured matrices will be introduced, the application of fast trigonometric transforms for multplication will be discussed and advanced iterative methods and preconditioners will be presented and analyzed.
In the winter term 2019/20 offered as a reading course.
Further information is available from Prof. Dr. Bolten.
Michael K. Ng. Iterative Methods for Toeplitz Systems. Oxford University Press, 2004.
Modul: Selected Topics in Numerical Analysis and Algorithm