Numerical Linear Algebra deals with fundamental problems of linear algebra from a numerical, i.e., applied point of view. The course introduces and discusses methods and techniques to solve a wide variety of computational tasks in linear algebra, such as the solution of linear systems of equations, the solution of least-squares problems and the computation of spectral properties of linear operators (e.g., the computation of eigenvalues and eigenvectors). Even though the theoretical foundation of these problems is discussed already in a linear algebra course their efficient solution is oftentimes very intricate. To overcome these difficulties a number of beautiful ideas and algorithms are introduced in this course which are typically not covered in a standard linear algebra course and which provide means to make the powerful concepts of linear algebra applicable in practice. Due to the importance of these topics in applications and their fundamental role in linear algebra, the course not only provides methods and techniques relevant to real world situations, but is also easily accessible with only basic knowledge of linear algebra and numerical analysis.
Numerical Linear Algebra, Lloyd N. Trefethen and David Bau, III.
Matrix Computations, Gene H. Golub and Charles F. Van Loan
Applied Numerical Linear Algebra, James W. Demmel
The course will be taught in English.
Basic knowledge of linear algebra and numerical analysis.
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Bachelor Angewandte Naturwissenschaften (Mathematik), Weiterführung Numerik