Theory and Applications of Algorithms

Open Topics: Wilfried Gansterer

Topics of Wilfried Gansterer (wilfried.gansterer (at) univie.ac.at) focus on various aspects of numerical algorithms. For these topics, interest in numerical algorithms and (large-scale) matrix computations as well as in high performance computing and parallel computing is usually required.

Please note: Below you find some examples of possible topics, but you can also contact me and suggest your own project idea!

  1. Robustness and fault tolerance in training and inference of (deep) neural networks (look here and here and here)
  2. State-of-the-art check-pointing for achieving fault tolerance in large-scale computations
  3. Fault tolerant iterative linear solvers
  4. Interpolation-based fault tolerance for the GMRES algorithm
  5. Exact state reconstruction for the GMRES algorithm
  6. Mixed-Precision linear solver for FPGAs:
    1. https://ieeexplore.ieee.org/document/4531732
    2. https://www.sciencedirect.com/science/article/abs/pii/S0167819120300569
  7. (Spectral) divide-and-conquer algorithms for solving large-scale eigenvalue problems
  8. Efficient sparse tensor decomposition (look here)
  9. Mixed Precision Low Rank Approximations and their Application to Block Low Rank LU Factorization
    1. https://hal.science/hal-03251738v1/document
  10. Replacing Pivoting in Distributed Gaussian Elimination with Random Techniques
    1. https://ieeexplore.ieee.org/document/9308659
  11. Quantization of rank-one matrices
    1. https://lip6.fr/Theo.Mary/doc/rank1quant.pdf
  12. Communication Avoiding ILU0 Preconditioner (look here)
  13. The power method in a dynamic setting (look here)