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We discuss the solution of eigenvalue problems associated with partialdifferential equations that can be written in the generalized form$\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend ona scalar parameter. Parameter dependent matrices occur frequently whenstabilized formulations are used for the numerical approximation of partialdifferential equations. With the help of classical numerical examples we showthat the presence of one (or both) parameters can produce unexpected results.

Approximation of PDE eigenvalue problems involving parameter dependent matrices