How Close Can the Logarithmic Norm of a Matrix Pencil Come to the Spectral Abscissa?
Inmaculada Higueras, Berta Garcı́a-Celayeta · SIAM Journal on Matrix Analysis and Applications · 2000
Given a least upper bound norm, the usefulness of the concept of logarithmic norm depends on how closely the logarithmic norm approximates the spectral abscissa. To study this problem, Ström introduced in 1975 the concepts of logarithmically optimal norm and $\varepsilon$-logarithmically optimal norm with respect to a matrix A. Recently Higueras and Garcia-Celayeta have done an extension of the concept of logarithmic norm for matrix pencils and, in a similar way, the usefulness of the concept depends on how closely the logarithmic norm of the pencil approximates the spectral abscissa. In this paper we study this problem and extend the concepts by Ström to matrix pencils.