Optimization and Systems Theory Seminar
Friday, Nov. 5, 1999, 11.00-12.00, Room 3721, Lindstedtsv. 25

Professor Lars Eldén
Department of Mathematics
Linköping University
Linköping, Sweden
E-mail: laeld@mai.liu.se

Solving constrained linear algebra problems using a differential geometric approach

In recent years development has taken place, where certain constrained problems in linear algebra are solved numerically using a differential geometric approach. Orthonormality constraints can be thought of as restrictions that the solution lies on the Stiefel or Grassmann manifold. Newton's method and the conjugate gradient method are formulated on the manifold, and are used in the actual numerical procedure.

We will illustrate the ideas using the quadratically constrained least squares problem min ||A x - b|| subject to xTx = 1, which occurs in the numerical solution of ill-conditioned linear problems, cf. also trust region methods in optimization. Numerical examples will be given showing that the Newton-Stiefel method converges faster than the standard approach. If time permits we will describe how manifold theory can be used in the analysis of a generalization of the abovementioned problem, the orthogonal Procrustes problem.

Calendar of seminars
Last update: October 22, 1999 by Anders Forsgren, anders.forsgren@math.kth.se.