Matrix tests for stability

Biswa Nath Datta's paper Stability and 
inertia (Linear Algebra and its Applications, Volumes 302-303, 1 
December 1999, Pages 563-600) mentions three approaches for real 
matrices: eigenvalue computation, Routh-Hurwitz, and Lyapunov eqn. 
The usual way of solving the  Lyapunov eqn numerically uses 
eigenvalue factorisation, but it can be solved without eigenvalues, 
as in the paper B.N. Datta & K. Datta, The matrix equation XA = A^TX 
and an associated algorithm for inertia and stability, Linear Algebra 
Appl. 97, 1987, 103­109. This might be a good starting point for an 
interval arithmetic stability tester.

From: Robert Piche (firstname.lastname@tut.fi)
http://math.tut.fi/~piche/