Computer Algorithms in Applied Mathematics
Please register for the seminar and provide a preference for a topic until Friday, September 3.
Although matrix multiplication is used in all areas of mathematics, computer science, and physics, to this day no optimal algorithm for its calculation is known. Contrary to natural intuition, in 1969, Volker Strassen devised a method that requires only O(n^2.8074) operations instead of O(n^3). This example demonstrates that many problems raised in "Introduction to Numerics" are not conclusively solved. In this seminar, we will address, among others, the following questions:
- How is the matrix exponential efficiently calculated?
- How does polynomial interpolation work in multiple dimensions?
- Is there a cg algorithm for non-symmetric matrices?
- Does Gauss quadrature generalize to multiple dimensions?
- What does the Newton method look like with constraints?
Seminar talks are given on Tuesday, 2 pm in room 3.23.2 in building E1.1. Each talk should be 45 minutes long with 10 minutes for questions.
- 19.12.: Padé method for computing the matrix exponential
- 09.01.: Simplex algorithm for integer optimization problems
- 16.01.: Newton's method for nonlinear optimization
- 30.01.: Conjugate Gradient method with Preconditioners
Seminar completion criteria
In order to pass the seminar, you must
- send me a version of your presentation 2 weeks before your talk
- meet for a discussion 1 week before your talk
- give a 45 minute talk on your topic
- attend all talks (you may miss a single talk)
- ask questions during the talks
For additional ECTS points, you have to write a 10 page report on your topic.