Numerical solution of isospectral flows

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...

Numerical Solution of Isospectral

In this paper we are concerned with the problem of solving numerically isospectral ows. These ows are characterized by the diierential equation L 0 = B(L);L]; L(0) = L 0 ; where L 0 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 ows, ...

Numerical solution of isospectral owsMari

Stabilization of Nonholonomic Systems Using Isospectral Flows

In this paper we derive and analyze a discontinuous stabilizing feedback for a Lie algebraic generalization of a class of kinematic nonholonomic systems introduced by Brockett. The algorithm involves discrete switching between isospectral and norm-decreasing ows. We include a rigorous analysis of the convergence. 1. Introduction. In this paper we present a stabilization algorithm for a Lie

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...