Diagonalization Matrix Method of Solving the First Problem of Hidden   Markov Model in Speech Recognition System
  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. 
R. Gnanajeyaraman, G.Seenivasan
cs.DS