Realization of a Special Case of Indeterminate Finite Summation in Computer-Based Simulations

In this paper, we propose two algorithms to realize a specific case of indeterminate finite summation operation introduced by multinomial theorem in computer-based simulations. One is the time-first algorithm, the realization of which can be temporally advantageous. The other is the space-first algorithm, of which the realization can be spatially advantageous. Our proposed algorithms are examined by simulations, and their efficiency and effectiveness are illustrated. Moreover, we also point out that, by appropriate modifications, these two algorithms can be generalized for more applications. The contributions in this paper can be used to solve a number of numerical computations of the indeterminate finite summations of series in computer-based simulations.