The Monte Carlo Methods and Quasi Monte Carlo Methods for Systems of Linear Algebraic Equations

The Monte Carlo methods,Quasi-Monte Carlo methods for solving Systems of Linear Algebraic Equations(SLAE),and the error,the convergence rate of each method were analyzed.The error was caused by three aspects:the truncation error,the methods per se,the pseudo-random number and low-discrepancy sequences not uniform.In respect of convergence rate,Monte Carlo methods did not depend on the scale of problems and the number of walks.Quasi-Monte Carlo methods did not depend on the scale of problems either,but depended on the number of walks.In addition,the conditions of using the Monte Carlo methods,Quasi-Monte Carlo methods and the numerical experiments discussed,Quasi-Monte Carlo methods were chosen to solve Linear Algebraic Equations(LAE) in general condition.