Newton's method for Monte Carlo-based residuals

Jeffrey Willert; Xiaojun Chen; C. T. Kelley

doi:10.1137/130905691

Newton's method for Monte Carlo-based residuals

Jeffrey Willert, Xiaojun Chen, C. T. Kelley

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1738-1757
Number of pages	20
Journal	SIAM Journal on Numerical Analysis
Volume	53
Issue number	4
DOIs	https://doi.org/10.1137/130905691
Publication status	Published - 1 Jan 2015

Keywords

JFNK methods
Monte Carlo simulation
Neutron transport
Newton's method

ASJC Scopus subject areas

Numerical Analysis

More information

10.1137/130905691

http://hdl.handle.net/10397/96241

Cite this

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AU - Kelley, C. T.

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AB - 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.

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KW - Monte Carlo simulation

KW - Neutron transport

KW - Newton's method

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DO - 10.1137/130905691

M3 - Journal article

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JF - SIAM Journal on Numerical Analysis

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Newton's method for Monte Carlo-based residuals

Abstract

Keywords

ASJC Scopus subject areas

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