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This paper proposes a computationally efficient method of solving evaluationproblem of Hidden Markov Model (HMM) with a given set of discrete observationsymbols, number of states and probability distribution matrices. Theobservation probability for a given HMM model is evaluated using an approach inwhich the probability evaluation is reduced to the problem of evaluating theproduct of matrices with different powers and formed out of state transitionprobabilities and observation probabilities. Finding powers of a matrix is doneby using the computationally efficient diagonalization method thereby reducingthe overall computational effort for evaluating the Evaluation problem ofHMM.The proposed method is compared with the existing direct method. It isfound that evaluating matrix power by diagnolisation method is more suitablethan that of the direct, method.

Diagonalization Matrix Method of Solving the First Problem of Hidden Markov Model in Speech Recognition System