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Week 6 Numerical Stability

The material in this chapter has be adapted from

  • [3] Paolo Bientinesi, Robert A. van de Geijn, Goal-Oriented and Modular Stability Analysis, SIAM Journal on Matrix Analysis and Applications , Volume 32 Issue 1, February 2011.

and the technical report version of that paper (which includes exercises)

  • [4] Paolo Bientinesi, Robert A. van de Geijn, The Science of Deriving Stability Analyses, FLAME Working Note #33. Aachen Institute for Computational Engineering Sciences, RWTH Aachen. TR AICES-2008-2. November 2008.

We recommend the technical report version for those who want to gain a deep understanding. Some of the materials in those papers has been used verbatim, with permission from the authors.

In this chapter, we focus on computation with real-valued scalars, vectors, and matrices.