 
Summary: 19 MAR 2006 To appear in Int. J. Unconventional Computing
Continuoustime systems that solve
computational problems
P.A. ABSIL12
1
Department of Mathematical Engineering, Universit´e catholique de Louvain,
1348 LouvainlaNeuve, Belgium. URL: http://www.inma.ucl.ac.be/absil/
2
Peterhouse, University of Cambridge, Cambridge CB2 1RD, UK.
The concept of using continuoustime dynamical systems (de
scribed by ordinary differential equations) in order to solve com
putational problems is discussed, with an emphasis on conver
gence analysis and design procedures. The continuoustime ap
proach is illustrated on concrete examples related to the compu
tation of eigenvalues and eigenvectors of matrices.
Key words: continuoustime systems, ordinary differential equations,
continuoustime algorithms, gradient flows, Rayleigh quotient gradient
flow, doublebracket flow, eigenvalue problem
1 INTRODUCTION
Many scientific computing algorithms (in various domains, such as weather
