Newton's method for Monte Carlo-based residuals

Jeffrey Willert, Xiaojun Chen, C. T. Kelley

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1738-1757
Number of pages20
JournalSIAM Journal on Numerical Analysis
Issue number4
Publication statusPublished - 1 Jan 2015


  • JFNK methods
  • Monte Carlo simulation
  • Neutron transport
  • Newton's method

ASJC Scopus subject areas

  • Numerical Analysis


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