Summary: 19 MAR 2006 To appear in Int. J. Unconventional Computing
Continuous-time systems that solve
Department of Mathematical Engineering, Universit´e catholique de Louvain,
1348 Louvain-la-Neuve, Belgium. URL: http://www.inma.ucl.ac.be/absil/
Peterhouse, University of Cambridge, Cambridge CB2 1RD, UK.
The concept of using continuous-time 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 continuous-time ap-
proach is illustrated on concrete examples related to the compu-
tation of eigenvalues and eigenvectors of matrices.
Key words: continuous-time systems, ordinary differential equations,
continuous-time algorithms, gradient flows, Rayleigh quotient gradient
flow, double-bracket flow, eigenvalue problem
Many scientific computing algorithms (in various domains, such as weather