Eigenvalue Problems and Applications

*Sponsored by SIAM Activity Group on Linear Algebra*

10:30 AM-12:30 PM

*Room: Capitol North*

Algebraic eigenvalue problems and their applications continue to be a
challenging yet fruitful area of research for numerical analysts.The
speakers will describe four diverse topics relating to the eigenvalue
problem: relative perturbation theory, implementation of the
multishift QR-algorithm, eigenvalue-based characterization of
positive realness of transfer functions, and solution of the
quadratic matrix equation AX^{2}+ BX + C = 0 associated with
the quadratic eigenvalue problem.

**Organizer: Nicholas J. Higham**

*University of Manchester, United Kingdom*

**10:30-10:55 A New Relative Perturbation Theorem for Singular Subspaces**- Ren-Cang Li, University of Kentucky; and
*G. W. Stewart*, University of Maryland, College Park **11:00-11:25 The Multishift QR-Algorithm: Aggressive Deflation, Maintaining Well Focused Shifts, and Level 3 Performance**

- Karen Braman and
*Ralph Byers*, University of Kansas, Lawrence

**11:30-11:55 Passivity and Eigenvalue Problems**

*Zhaojun Bai*, University of Kentucky; and Roland Freund, Bell Laboratories, Lucent Technologies

**12:00-12:25 Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches**

*Nicholas J. Higham*, Organizer; and Hyun-Min Kim, University of Manchester, United Kingdom

*tjf, 1/20/99, MMD, 4/30/99*