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Stable Type

A Polynomial equation whose Roots all have Negative Real Parts. For a Real Quadratic Equation

\begin{displaymath}
z^2+Bz+C=0,
\end{displaymath}

the stability conditions are $B,C>0$. For a Real Cubic Equation

\begin{displaymath}
z^3+Az^2+Bz+C=0,
\end{displaymath}

the stability conditions are $A,B,C>0$ and $AB>C$.


References

Birkhoff, G. and Mac Lane, S. A Survey of Modern Algebra, 3rd ed. New York: Macmillan, pp. 108-109, 1965.




© 1996-9 Eric W. Weisstein
1999-05-26