# Solution of the First Underwood Equation Formulated as a Generalized Eigenvalue Problem

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The solution to the familiar eigenvalue problem is routinely taught in undergraduate linear algebra courses, but it is rare that the generalized eigenproblem is discussed, often because of a lack of suitable physical examples where such problems arise. In this Demonstration we show how a familiar distillation problem in undergraduate chemical engineering can be reformulated as a generalized eigenvalue problem to find the roots of an -order polynomial.

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Contributed by: Housam Binous and Brian G. Higgins (December 2012)

Open content licensed under CC BY-NC-SA

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References

[1] R. Monroy-Loperena and M. Vacahern, "Roots of the Underwood's Equations in Short-Cut Distillation from a Companion Matrix Eigenvalues," *Chemical Engineering Science*, 76(1), 2012 pp. 9–13. doi:10.1016/j.ces.2012.03.025.

[2] R. Monroy-Loperena and F. D. Vargas-Villamil, "Determination of the Polynomial Defining Underwood's Equations in Short-Cut Distillation Design," *Industrial and Engineering Chemical Research*, 40(24), 2001 pp. 5810–5814. doi:10.1021/ie010091o.

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