A Levenberg-Marquardt iterative solver for least-squares problems

Communications in Numerical Methods in Engineering

Volumn 21, Issue 6, 2005, Pages 327-335

  Ho, H W ^a   Wong, S C ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Iterative solver; Least squares problem; Levenberg Marquardt; Trust region

Indexed keywords

LEAST SQUARES APPROXIMATIONS; NUMERICAL ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

COMPUTING TIME; LARGE-SCALE PROBLEMS; LEAST-SQUARE PROBLEMS; LEVENBERG-MARQUARDT ITERATIVE SOLVER;

ITERATIVE METHODS;

MATHEMATICAL METHOD;

EID: 20444452359     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.757     Document Type: Article

References (13)

1. Dennis JE, Schnabel RB. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM: Philadelphia, PA, 1996.
2. Fletcher R. Practical Methods of Optimization (2nd edn). Wiley: New York, 1987.
3. Levenberg K. A method for the solution of certain nonlinear problem in least squares. Quarterly of Applied Mathematics 1944; 2: 164-168.
4. Marquardt DW. Solution of nonlinear chemical engineering models. Chemical Engineering Progress 1959; 55: 65-70.
5. Kelley CT. Iterative Methods fbr Optimization. SIAM: Philadelphia, PA, 1999.
6. Moré JJ. The Levenberg-Marquardt algorithm: implementation and theory. In Numerical Analysis, Lecture Notes in Mathematics, Watson GA (ed.), vol. 630. Springer: Berlin, 1977; 105-116.
7. Hageman LA, Young DM. Applied Iterative Methods. Academic Press: New York, 1981.
8. Young DM. Iterative Solution of Large Linear System. Academic Press: New York, 1971.
9. Moré JJ, Garbow BS, Hillstorm KE. Testing unconstrained optimization software. ACM Transactions on Mathematical Software 1981; 7: 136-140.
10. Harwell Subroutine Library Specification (Release 12) Volume 1 & 2, AEA Technology, Harwell Laboratory, Oxfordshire, 1995.
11. Bard YB. Nonlinear Parameter Estimation in Engineering and Science. Wiley: New York, 1977.
12. IMSL Library, Edition 10, NBC Bldg., 7500 Ballaire Blvd., Houston, TX, 1987.
13. Press WH, Flannery BF, Teukolsky SA, Wetterling WT. Numerical Recipes. Cambridge University Press: New York, 1989.