Some Further Results on Optimal Scaling

We present some new results on optimal scaling - i.e., the design of a diagonal matrix K so as optimize the product KG, G isin R_ntimesn, with respect to a performance measure. In particular, we extend our previous work on optimizing the dominant eigenvalue ratio to three other performance measures: 1) the condition number, 2) the ratio of the minimum eigenvalue to the infinity-norm of KG, and 3) a Lyapunov exponent-based measure. We also give some preliminary explorations into eigenvalue placement through scaling