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A counterexample for two conjectures about stability

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1 Author(s)
Demmel, J.W. ; Courant Institute of Mathematics, New York, NY, USA

One measure of the stability of a matrixAis the distance to the nearest unstable matrixB. Recently Van Loan presented an algorithm to computeBwhich depended on a conjecture about the location of its eigenvalues. We provide a counterexample to this conjecture which shows that the algorithm may overestimate the distance toBby an arbitrary amount. The same counterexample invalidates another conjecture and algorithm of the author.

Published in:

Automatic Control, IEEE Transactions on  (Volume:32 ,  Issue: 4 )

Date of Publication:

Apr 1987

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