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.
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  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.