Lie–Poisson Methods for Isospectral Flows

Semi-explicit methods for isospectral flows

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L′ = [B,L] for d × d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying flow. We present techniques that allow us to decrease the bre...

University of Cambridge Lie-group Methods for Isospectral Flows

Isospectral Flows for Displacement Structured Matrices

This paper concernes eigenvalue computations with displacement structured matrices, for example, Toeplitz or Toeplitz-plus-Hankel. A technique using isospectral flows is introduced. The flow is enforced to preserve the displacement structure of the originary matrix by means of a suitable constraint added in its formulation. In order to fulfil the constraint, the numerical integration of the flo...

Numerical solution of isospectral flows

In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation L′ = [B(L), L], L(0) = L0, where L0 is a d × d symmetric matrix, B(L) is a skew-symmetric matrix function of L and [B,L] is the Lie bracket operator. We show that standard Runge–Kutta schemes fail in recovering the main qualitative feature of these...

University of Cambridge Semi-explicit Methods for Isospectral Ows Semi-explicit Methods for Isospectral Ows

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L 0 = B; L] for d d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying ow. We present techniques that allow us to decrease the breakd...