Low-rank Tensor Discretization for High-Dimensional Problems
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
MA5904 is a semester module in English language at Master’s level which is offered irregular.
This module description is valid from WS 2016/7 to SS 2017.
|Total workload||Contact hours||Credits (ECTS)|
|90 h||30 h||3 CP|
Content, Learning Outcome and Preconditions
- Tensor approximations in hierarchical Tucker and tensor train format
- Tensor operations in hierarchical Tucker and tensor train format
- Generalized cross approximation
- Alternating least squares method and the solution of low-rank linear systems
- Applications to approximation of high-dimensional partial differential equations and parametric partial differential equations
- Programming exercises in Matlab
- understand the concept of low-rank tensor approximation, algorithms for the approximation of high-dimensional tensors, and the implementation of basic tensor operations.
- compare various low-rank tensor formats and algorithms,
- design Matlab programs for the approximation of multi-variate functions, the solution of high-dimensional partial differential equations or the quantification of uncertainties based on a low-rank tensor representation of the solution.
Courses, Learning and Teaching Methods and Literature
Learning and Teaching Methods
Tensor Calculus, Springer, 2012.
Description of exams and course work
The exam may be repeated at the end of the semester.