Yousong Luo

Yousong Luo; Robin Hill

Abstract In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

Robin Hill; Yousong Luo; Uwe Schwerdtfeger

Abstract In this paper we illustrate some new ideas in the theory of l 1 –norm minimisation. A simple looking mathematical programming problem, namely the minimisation of the sum of the one norms of two signals connected by convolution constraints, is investigated. This describes an l 1 model matching problem for which there are no zero interpolation conditions, and just one rank interpolation condition. Despite its apparent simplicity, finding exact solutions for this problem is a challenging task. We extend the class of problems for which exact optimal solutions can be found by combining a primal/dual formulation with dynamic programming ideas. These solutions have the desirable feature of yielding a control law in feedback form.

Yousong Luo

We prove uniqueness of the viscosity solutions of the Dirichlet problem of the spectral equation

Robin Hill; Yousong Luo; Uwe Schwerdtfeger

Yousong Luo; Andrew Eberhard

F(u)=f(\lambda[u])=\psi

Robin Hill; Uwe Schwerdtfeger; Michael Baake; Yousong Luo

Robin Hill; Yousong Luo; Uwe Schwerdtfeger

where

Yousong Luo

Robin Hill; Yousong Luo

\lambda[u]

Yousong Luo