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Title: Levenberg--Marquardt algorithm: implementation and theory

Levenberg--Marquardt algorithm: implementation and theory The nonlinear least-squares minimization problem is considered. Algorithms for the numerical solution of this problem have been proposed in the past, notably by Levenberg (Quart. Appl. Math., 2, 164-168 (1944)) and Marquardt (SIAM J. Appl. Math., 11, 431-441 (1963)). The present work discusses a robust and efficient implementation of a version of the Levenberg--Marquardt algorithm and shows that it has strong convergence properties. In addition to robustness, the main features of this implementation are the proper use of implicitly scaled variables and the choice of the Levenberg--Marquardt parameter by means of a scheme due to Hebden (AERE Report TP515). Numerical results illustrating the behavior of this implementation are included. 1 table. (RWR)
Authors:
Publication Date:
OSTI Identifier:7256021
Report Number(s):CONF-770636-1
DOE Contract Number:W-31-109-ENG-38
Resource Type:Conference
Data Type:
Resource Relation:Conference: Conference on numerical analysis, Dundee, UK, 28 Jun 1977
Research Org:Argonne National Lab., IL (USA)
Country of Publication:United States
Language:English
Subject: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; LEAST SQUARE FIT; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; SERIES EXPANSION; MATHEMATICAL LOGIC; MAXIMUM-LIKELIHOOD FIT 990200* -- Mathematics & Computers