Quasi-Newton methods for large-scale electromagnetic inverse problems

Inverse Problems

Volumn 21, Issue 1, 2005, Pages 305-323

  Haber, E ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; INVERSE PROBLEMS; MAGNETIC SUSCEPTIBILITY; MATHEMATICAL MODELS; MAXWELL EQUATIONS; NONLINEAR EQUATIONS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING;

JACOBIAN TIMES; QUASI-NEWTON METHODS; REALISTIC MODEL PROBLEMS; TIKHONOV PROBLEMS;

ELECTROMAGNETIC WAVES;

EID: 13744252043     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/1/019     Document Type: Article

References (44)

1. Ascher U and Haber E 2003 A multigrid method for distributed parameter estimation problems ETNA 15 1-15
2. Barrett R, Berry M, Chan T F, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C and Van der Vorst H 1994 Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (Philadelphia, PA: SIAM)
3. Bishp J, Carroll N and Macinnes S 1997 Finding sphalerite at broken hill drillhole meat Expl. Geophys. 28 6-10
4. Borcea L 2001 Nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency Inverse Problems 17 329-60
5. Borcea L 2002 Electrical impedance tomography Inverse Problems 18 99-136
6. Chan J, Haber E and Oldenburg D 2002 Three-dimensional numerical modelling and inversion of magnetometric resistivity data Geophys. J. Int. 149 679-97
7. Chavent G 1989 A non-linear least-square theory for inverse problems Inverse Methods in Action ed P Sabatier (Berlin: Springer)
8. Dennis J and More J 1977 Quasi newton methods, methods, motivation and theory SIAM Rev. 19 46-89
9. Dennis J E and Schnabel R B 1996 Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Philadelphia, PA: SIAM)
10. Dennis J E and Walker H F 1981 Convergence theorems for least-change secant update methods SIAM Num. Anal. 18 949-87
11. Dom O 2000 A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets Inverse Problems 16 1119-56
12. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
13. Gilles Luc, Vogel C R and Bardsley J M 2002 Computational methods for a large-scale inverse problem arising in atmospheric optics Inverse Problems 18 237-52
14. Haber E 1997 Numerical strategies for the solution of inverse problems PhD Thesis University of British Columbia
15. Haber E, Ascher U, Aruliah D and Oldenburg D 2000 Fast simulation of 3D electromagnetic using potentials J. Comput. Phys. 163 150-71
16. Haber E, Ascher U and Oldenburg D 2000 On optimization techniques for solving nonlinear inverse problems Inverse problems 16 1263-80
17. Haber E, Ascher U and Oldenburg D 2004 Inversion of frequency and time domain electromagnetic data Geophysics 69 1216-28
18. Haber E, Oldenburg D and Ascher U 2000 Inversion of 3D electromagnetic data - a constrained optimization approach SEG (Calgary, August 2000)
19. Haber E and Tenorio L 2003 Learning regularization functional a supervised training approach Inverse Problems 19 611-26
20. Hansen P C 1998 Rank Deficient and Ill-Posed Problems (Philadelphia, PA: SIAM)
21. Heinkenschloss M and Vicente L N 1999 Analysis of inexact trust region SQP algorithms Technical Report TR 99-18 Rice University
22. Hohage T 2001 On the numerical solution of a three-dimensional inverse medium scattering problem Inverse Problem 17 1743-63
23. Huber P J 1964 Robust estimation of a location parameter Ann. Math. Stat. 35 73-101
24. Ito K and Kunisch K 1990 The augmented Lagrangian method for parameter estimation in elliptic systems SIAM J. Control Opt. 28 113-36
25. Kaltenbacher B 1998 On Broydens method for regularization of nonlinear ill-posed problems Numer. Funct. Anal. Opt. 19 807-33
26. Kelley C T and Sachs E W 1987 Quasi-Newton methods and unconstrained optimal control problems SIAM J. Control Opt. 25 1503-17
27. Kelley C T and Sachs E W 1989 A pointwise quasi-Newton method for unconstrained optimal control problems Numer. Math. 55 159-76
28. Kelley C T and Sachs E W 1990 Approximate quasi-Newton methods Math. Program. B 48 41-70
29. Kelley C T and Sachs E W 1998 Local convergence of the symmetric rank-one iteration Comput. Opt. Appl. 9 43-63
30. Kelley C T, Sachs E W and Watson B 1991A pointwise quasi-Newton method for unconstrained optimal control problems J. Opt. Theor. Appl. 71 535-47
31. Knapek S 1999 Matrix-dependent multigrid homogenization for diffusion problems SIAM J. Sci. Comput. 20 515-33
32. Li Y and Oldenburg D W 1994 Inversion of 3-d dc resistivity data using an approximate inverse mapping Geophys. J. Int. 116 557-69
33. Mackie R L, Madden T R and Wannamaker P E 1993 Three dimensional magnetotelluric modeling using difference equations-theory and comparison to integral equation solutions Geophysics 58 215-26
34. Menke W 1989 Geophysical Data Analysis: Discrete Inverse Theory (San Diego, CA: Academic)
35. Nabighian M, Oppliger G, Edwards R, Lo B and Cheesman S 1984 Cross-hole magnetometric resistivity (MMR) Geophysics 49 1313-23
36. Nocedal J and Wright S 1999 Numerical Optimization (New York: Springer)
37. Parker R L 1994 Geophysical Inverse Theory (Princeton, NJ: Princeton University Press)
38. Pidlisecky A, Haber E and Knight R 2003 An assessment of feasibility of cone penetrometer based resistivity imaging system Proc. Symp. on the Application of Geophysics to Engineering and Environmetal Problems (6-10 April 2003, San Antonio, TX)
39. Tarantola A 1987 Inverse Problem Theory (Amsterdam: Elsevier)
40. Trottenberg U, Oosterlee C and Schuller A 2001 Multigrid (New York: Academic)
41. Vogel C 2001 Computational Methods for Inverse Problem (Philadelphia, PA: SIAM)
42. Wahba G 1990 Spline Models for Observational Data (Philadelphia, PA: SIAM)
43. Ward S H and Hohmann G W 1988 Electromagnetic theory for geophysical applications Electromagn. Methods Appl. Geophys. 1 131-311
44. Wilt M, Alumbaugh D, Morrison H, Becker A, Lee K and Deszcz-Pan M 1995 Crosswell electromagnetic tomography: system design considerations Geophysics 60 871-85