Hidden Markov Model is a popular statisical method that is used in continious and discrete speech recognition. The probability density function of observation vectors in each state is estimated with discrete density or continious density modeling. The performance (in correct word recognition rate) of continious density is higher than discrete density HMM, but its computation complexity is very ...

Light going through a participating medium like smoke can be scattered or absorbed by every point in the medium. To accurately render such a medium we must compute the radiance resulting at every point inside the medium because of these physical effects, which have been modeled by the radiative transfer equation. Computing the radiance at any point inside a participating medium amounts to numer...

Nakajima and Tanaka showed that the algebraic eigenvalue problem occurring in the discrete ordinate and matrix operator methods can be reduced to finding eigenvalues and eigenvectors of the product of two symmetric matrices, one of which is positive definite. Here, we show that the Cholesky decomposition of this positive definite matrix can be used to convert the eigenvalue problem into one inv...