Helmke, Uwe (Univ. of Wuerzburg), Jordan, Jens (Univ. of Wuerzburg), Lanzon, Alexander (The Australian National Univ.)

A Control Theory Approach to Linear Equation Solvers

Scheduled for presentation during the Mini-Symposium "Geometric Optimisation in Systems and Control I" (WeA07), Wednesday, July 26, 2006, 10:50−11:15, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

We present a new iterative approach for solving linear systems of equations. Our method is inspired by feedback stabilization schemes from robust control and yields a control system, whose parameters can be tuned to achieve prescribed convergence properties. In contrast to well-known iterative solution methods for linear equations from linear algebra, such as GMRES(m) or Arnoldi's method, the proposed dynamical systems solution algorithms have the advantage of being globally convergent or having tunable convergence properties.