β Scribed by L. Lopez
No coin nor oath required. For personal study only.
In recent years differential systems whose solutions evolve on manifolds of matrices have acquired a certain relevance in numerical analysis. A classical example of such a differential system is the well-known Toda flow. This paper is a partial survey of numerical methods recently proposed for approximating the solutions of ordinary differential systems evolving on matrix manifolds. In particular, some results recently obtained by the author jointly with his co-workers will be presented. We will discuss numerical techniques for isospectral and isodynamical flows where the eigenvalues of the solutions are preserved during the evolution and numerical methods for ODEs on the orthogonal group or evolving on a more general quadratic group, like the symplectic or Lorentz group. We mention some results for systems evolving on the Stiefel manifold and also review results for the numerical solution of ODEs evolving on the general linear group of matrices.
π SIMILAR VOLUMES
A measure of the stability properties of numerical integration methods for ordinary differential equations is provided by their stability region, which is that region in the complex (AtX) plane for which a given method is stable when applied to the differential equation with a time-step At. Free pa