Author: Danny C. Sorensen
        Dept. Computational and Applied Mathematics
        Rice University
        Houston, TX 77251-1892

Applications of Implicit Restarting in Optimization and Control


Implicit restarting is a technique for combining the implicitly
shifted QR mechanism with a k-step Arnoldi or Lanczos factorization
to obtain a truncated form of the implicitly shifted QR-iteration
suitable for large scale eigenvalue problems.  The software package ARPACK 
based upon this technique has been successfully used to solve
large scale symmetric and nonsymmetric (generalized) eigenvalue problems
arising from a variety of applications.

Recently, the implicit restarting technique has been applied to
problems in control and optimization.  The technique has been
generalized to provide an implicit restarting technique for the nonsymmetric
two sided Lanczos process.  This mechanism is used to obtain
stable reduced models for state space control systems.  Implicit restarting
has also found application in the numerical solution of
large scale trust region subproblem: Minimize a quadratic function
subject to an ellipsoidal constraint.

This talk will survey the applications in control and optimization.