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Computing mountain passes is a standard way of finding critical points. Wedescribe a numerical method for finding critical points that is convergent inthe nonsmooth case and locally superlinearly convergent in the smooth finitedimensional case. We apply these techniques to describe a strategy for theWilkinson problem of calculating the distance of a matrix to a closest matrixwith repeated eigenvalues. Finally, we relate critical points of mountain passtype to nonsmooth and metric critical point theory.

Level set methods for finding critical points of mountain pass type