Jump to ContentJump to Main Navigation
Numerical Methods for Nonlinear Estimating Equations$
Users without a subscription are not able to see the full content.

Christopher G. Small and Jinfang Wang

Print publication date: 2003

Print ISBN-13: 9780198506881

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198506881.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 19 July 2019

Numerical algorithms

Numerical algorithms

(p.37) 3 Numerical algorithms
Numerical Methods for Nonlinear Estimating Equations

Christopher G. Small

Jinfang Wang

Oxford University Press

This chapter surveys a variety of root-finding and hill-climbing algorithms that are useful for solving estimating equations or maximizing artificial likelihoods, starting with a basic technique known as the iterative substitution. Methods such as the Newton-Raphson and the quasi-Newton algorithms are motivated as attempts to improve the rate of convergence of the iterative substitution. The contractive mapping theorem, which provides general conditions for the convergence of a multiparameter algorithm, is stated and proved. The EM-algorithm is described in generality and illustrated with examples. Aitken's method for accelerating linear convergence of algorithms is developed, along with a refinement known as Steffensen's method. Other methods discussed in this chapter include the method of false positions, Muller's method, methods particularly suitable for solving polynomial equations (such as the Bernoulli's method, the quotient-difference algorithm, Sturm's method and the QR-algorithm), the Nelder-Mead algorithm, and the method of Jacobi iteration for approximate inversion of matrices.

Keywords:   Aitken's method, Bernoulli's method, EM-algorithm, iterative substitution, Muller's method, quotient-difference algorithm, Nelder-Mead algorithm, Newton-Raphson algorithm, Sturm's method, QR-algorithm, Steffensen's method

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .