NOVEL APPROACH FOR EIGENVALUE PROBLEMS USING THE MONTE CARLO METHOD

In this paper, we have studied various types of Monte Carlo methods along with the Power method to evaluate the maximum and minimum eigenvalue of a linear system of equations. We have studied how the accuracy of the maximum eigenvalue depends on the parameters, e (moves in Markova chain), K (no of Markova chain), p (accelerating parameter), and a parameter m (the power applied on the resolving matrix). We have applied these methods to the randomly chosen symmetric matrices. We have also made comparisons for the different matrices of different orders depending on the parameters by using the Monte Carlo methods. We are Matlab 2020R the calculation.