  This paper proposes a computationally efficient method of solving evaluation
problem of Hidden Markov Model (HMM) with a given set of discrete observation
symbols, number of states and probability distribution matrices. The
observation probability for a given HMM model is evaluated using an approach in
which the probability evaluation is reduced to the problem of evaluating the
product of matrices with different powers and formed out of state transition
probabilities and observation probabilities. Finding powers of a matrix is done
by using the computationally efficient diagonalization method thereby reducing
the overall computational effort for evaluating the Evaluation problem of
HMM.The proposed method is compared with the existing direct method. It is
found that evaluating matrix power by diagnolisation method is more suitable
than that of the direct, method.
