Enhancing the Performance of Stochastic Iterative Projection Methods Using Quasi Random Numbers for Solving Linear Algebra Problems

Solving linear algebraic equations (SLAE) is significantly important in many science and engineering areas as well as communication and physics problems. In this paper, the principal method for solving linear equation system is the Kaczmarz method, its stochastic model, and also stochastic block method, which are based on the random selection of rows or blocks of the desired matrix. Furthermore, a quasi-random sequence is employed in these methods to improve the uniformity of basic random number generators in the Monte Carlo simulation, and it is shown that the low-discrepancy sequences improve the efficiency of proposed methods. In fact, it is shown that employing a quasi-random number generator provides stability of the computation. Moreover, in this paper, an approach for calculating the inverse matrix based on the Kaczmarz method with high accuracy is used.

Keywords:

Kaczmarz method , Linear equation system , Quasi-random number , Randomized projection methods