Title: Computing matrix eigenvalues
Speaker: Yuji Nakatsukasa, National Institute for Informatics, Japan
The numerical linear algebra community solves two main problems: linear
systems, and eigenvalue problems. They are both vastly important; it
would not be too far-fetched to say that most (continuous) problems in
scientific computing eventually boil down to one or both of these.
This talk focuses on eigenvalue problems. I will first describe some of
its applications, such as Google’s PageRank, PCA, finding zeros and
poles of functions, and nonlinear and global optimization. I will then turn to
algorithms for computing eigenvalues, namely the classical QR
algorithm—which is still the basis for state-of-the-art. I will
emphasize that the underlying mathematics is (together with the power
method and numerical stability analysis) rational approximation theory.