Obtaining minimal Gerschgorin discs by scaling the states
T. Walley Williams · International Journal of Control · 1985
The numerical performance of many linear algebra algorithms (even numerically stable ones) can be significantly improved by proper initial scaling of the matrices they operate on. In the case of state-space representations, the most difficult aspect of this is finding appropriate scaling for the system states. This problem is studied here, and a new numerically reliable scaling algorithm is derived which minimizes the Gerschgorin discs of the matrix A, so yielding tight eigenvalue bounds in a computationally cheap way. Examples are used to illustrate the superiority of this algorithm over existing methods.