  Piecewise smooth maps are known to exhibit a wide range of dynamical features
including numerous types of periodic orbits. Predicting regions in parameter
space where such periodic orbits might occur and determining their stability is
crucial to characterize the dynamics of the system. However, obtaining the
conditions of existence and stability of these periodic orbits generally use
brute force methods which require successive application of the iterative map
on a starting point. In this article, we propose a faster and more elegant way
of obtaining those conditions without iterating the complete map. The method
revolves around direct computation of higher powers of matrices without
computing the lower ones and is applicable on any dimension of the phase space.
In the later part of the article, we compare the speed of the proposed method
with the other popular algorithms which shows the effectiveness of the proposed
method in higher dimensions. We also illustrate the use of this method in
computing the regions of existence and stability of a particular class of
periodic orbits in three dimensions.
