This paper extends the implicit determinant method introduced by Spence & Poulton (2005, J. Comput. Phys., 204, 65–81) to obtain a numerical technique for the calculation of a two-dimensional Jordan block in a parameter-dependent matrix. An important feature of this technique is that the theory is straightforward to understand and an efficient numerical implementation is suggested naturally by the theory. Three interesting physical problems are presented, arising from the panel flutter problem in aerodynamics, the stability of electrical power systems and a problem in quantum mechanics.
Akinola, R. O., Freitag, M. A., & Spence, A. (2014). The computation of Jordan blocks in parameter-dependent matrices. IMA Journal of Numerical Analysis, 34(3), 955-976. https://doi.org/10.1093/imanum/drt028