Approximate iterative methods for variational data assimilation

International Journal for Numerical Methods in Fluids

Volumn 47, Issue 10-11, 2005, Pages 1129-1135

  Lawless, A S ^a   Gratton, S ^b   Nichols, N K ^a  

^a UNIVERSITY OF READING   (United Kingdom)

^b CERFACS   (France)

Author keywords

Data assimilation; Gauss Newton

Indexed keywords

APPROXIMATION THEORY; DATA ACQUISITION; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING;

DATA ASSIMILATIONS; GAUSS-NEWTON METHOD; NON-LINEAR LEAST SQUARES PROBLEMS;

ITERATIVE METHODS;

MATHEMATICAL ANALYSIS;

EID: 16344394714     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.851     Document Type: Article

References (10)

1. Courtier P, Thepaut J-N, Hollingsworth A. A strategy for operational implementation of 4D-Var, using an incremental approach. Quarterly Journal of the Royal Meteorological Society 1994; 120:1367-1387.
2. Lawless AS, Gratton S, Nichols NK. An investigation of incremental 4D-Var using non-tangent linear models. Quarterly Journal of the Royal Meteorological Society, to appear.
3. Dennis JE, Schnabel R. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall: Englewood Cliffs, NJ, 1983.
4. Ortega JM, Rheinboldt WC. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press: New York, 1970.
5. Wedin P-Å. On the Gauss Newton method for the nonlinear least-squares problem. Working Paper 24, Institute for Applied Mathematics, Stockholm, Sweden, 1974.
6. Lawless AS, Nichols NK, Ballard SP. A comparison of two methods for developing the linearization of a shallow water model. Quarterly Journal of the Royal Meteorological Society 2003; 129:1237-1254.
7. Dembo RS, Eisenstat SC, Steihaug T. Inexact Newton methods. SIAM Journal on Numerical Analysis 1982; 19(2):400-408.
8. Gratton S, Lawless AS, Nichols NK. Approximate Gauss-Newton methods for nonlinear least squares problems. Numerical Analysis Report 9/04, Department of Mathematics, The University of Reading, 2004.
9. Veersé F, Thépaut J-N. Multiple-truncation incremental approach for four-dimensional variational data assimilation. Quarterly Journal of the Royal Meteorological Society 1998; 124:1889-1908.
10. Cǎtinaş E. Inexact perturbed Newton methods and applications to a class of Krylov solvers. Journal of Optimization Theory and Applications 2001; 108(3):543-571.