Talks - Matthias Petschow

  1. MRRR-Based Eigensolvers for Multi-Core Processors and Supercomputers
    RWTH Aachen, Schinkelstr. 2, 52062 Aachen, December 2013.
    Doctoral defense.
    The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for dense standard and generalized Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR or MR^3 in short) - introduced in the late 1990s - is among the fastest methods. To compute k eigenpairs of an n-by-n tridiagonal T, MRRR only requires O(kn) arithmetic operations; in contrast, all the other practical methods require O(k^2 n) or O(n^3) operations in the worst case. This talk centers around the performance and accuracy of MRRR-based eigensolvers on modern parallel architectures.
  2. Orthogonality in the Hermitian Eigenproblem and the MRRR Algorithm
    International Workshop on Parallel Matrix Algorithms and Applications (PMAA 2012).
    London, England, June 2012.
  3. The Symmetric Tridiagonal Eigenproblem on Massively-Parallel Supercomputers
    International Linear Algebra Society Conference (ILAS 2011).
    Braunschweig, Germany, August 2011.
  4. The Algorithm of Multiple Relatively Robust Representations for Multi-Core Processors
    International Workshop on Parallel Matrix Algorithms and Applications (PMAA 2010).
    Basel, Switzerland, June 2010.
  5. An Example of Symmetry Exploitation for Energy-related Eigencomputations
    International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2009).
    Rethymno, Crete, Greece, September 2009.