An alternative analytical exact solution for the discrete-size kinetic equation of grinding in cumulative-fraction-passing mode was formulated as a matrix equation and tested successfully for predicting the transient evolution of the cumulative particle-size distribution and also for back-calculating the selection and breakage function parameters. The compact matrix form of the equation makes it computationally simple, and easy to extend the treatment to continuous mills. The solution should be particularly useful for parameter estimation purposes as it is expected to reduce the variability of the estimates because of the monotonic nature of the cumulative size distributions. (c) 2004 Elsevier Ltd. All rights reserved.