Newton's Method for Monte Carlo--Based Residuals

Jeffrey Willert, Xiaojun Chen, C. T. Kelley
2015 SIAM Journal on Numerical Analysis  
We analyze the behavior of inexact Newton methods for problems where the nonlinear residual, Jacobian, and Jacobian-vector products are the outputs of Monte Carlo simulations. We propose algorithms which account for the randomness in the iteration, develop theory for the behavior of these algorithms, and illustrate the results with an example from neutronics.
doi:10.1137/130905691 fatcat:ojes4mmxwbaqbdkpysdvpqwbey