  In the broad context of physics ranging from classical experimental optics to
quantum mechanics of unitary as well as non-unitary systems there emerge
interesting phenomena related to the presence of the so called Kato's
exceptional points in the space of parameters. An elementary linear-algebraic
method of their localization is proposed and applied to the class of
tridiagonal $N$ by $N$ complex symmetric toy-model generators of evolution
$H=H(\gamma)$. The implementation of the method is shown to provide new models
with the exceptional points $\gamma=\gamma^{(EP)}$ of higher orders. Two
distinct areas of applicability are expected to lie (1) in quantum mechanics of
non-Hermitian (open as well as closed) systems, and (2) in the experiments
using the coupled classical optical waveguides simulating the EP-related
effects in the laboratory.
