Brockett has studied the isospectral flow H=[H,[H,N]], with [A,AB-BA], on spaces of real symmetric matrices. The flow diagonalises real symmetric matrices and can be used to solve linear programming problems with compact convex constraints. The authors show that the flow converges exponentially fast to the optimal solution of the programming problem and they give explicit estimates for the time needed by the flow to approach an epsilon-neighbourhood of the optimum. An interior point algorithm for the standard simplex is analysed in detail and a comparison is made with a continuous time version of Karmarkar algorithm.
