Free Access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 689 - 708
DOI https://doi.org/10.1051/m2an/2009025
Published online 08 July 2009
  1. H. Akaike, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann. Inst. Stat. Math. Tokyo 11 (1959) 1–16. [CrossRef] [Google Scholar]
  2. U. Ascher, Numerical Methods for Evolutionary Differential Equations. SIAM, Philadelphia, USA (2008). [Google Scholar]
  3. U. Ascher, E. Haber and H. Huang, On effective methods for implicit piecewise smooth surface recovery. SIAM J. Sci. Comput. 28 (2006) 339–358. [CrossRef] [MathSciNet] [Google Scholar]
  4. U. Ascher, H. Huang and K. van den Doel, Artificial time integration. BIT 47 (2007) 3–25. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Barzilai and J. Borwein, Two point step size gradient methods. IMA J. Num. Anal. 8 (1988) 141–148. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Cheney, D. Isaacson and J.C. Newell, Electrical impedance tomography. SIAM Review 41 (1999) 85–101. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Chung, T. Chan and X. Tai, Electrical impedance tomography using level set representations and total variation regularization. J. Comp. Phys. 205 (2005) 357–372. [CrossRef] [MathSciNet] [Google Scholar]
  8. Y. Dai and R. Fletcher, Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming. Numer. Math. 100 (2005) 21–47. [CrossRef] [MathSciNet] [Google Scholar]
  9. Y. Dai, W. Hager, K. Schittkowsky and H. Zhang, A cyclic Barzilai-Borwein method for unconstrained optimization. IMA J. Num. Anal. 26 (2006) 604–627. [CrossRef] [Google Scholar]
  10. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems. Kluwer (1996). [Google Scholar]
  11. M. Figueiredo, R. Nowak and S. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1 (2007) 586–598. [CrossRef] [Google Scholar]
  12. G.E. Forsythe, On the asymptotic directions of the s-dimensional optimum gradient method. Numer. Math. 11 (1968) 57–76. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Friedlander, J. Martinez, B. Molina and M. Raydan, Gradient method with retard and generalizations. SIAM J. Num. Anal. 36 (1999) 275–289. [CrossRef] [Google Scholar]
  14. G. Golub and Q. Ye, Inexact preconditioned conjugate gradient method with inner-outer iteration. SIAM J. Sci. Comp. 21 (2000) 1305–1320. [CrossRef] [MathSciNet] [Google Scholar]
  15. A. Greenbaum, Iterative Methods for Solving Linear Systems. SIAM, Philadelphia, USA (1997). [Google Scholar]
  16. E. Haber and U. Ascher, Preconditioned all-at-one methods for large, sparse parameter estimation problems. Inverse Problems 17 (2001) 1847–1864. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Second Edition, Springer (1996). [Google Scholar]
  18. H. Huang, Efficient Reconstruction of 2D Images and 3D Surfaces. Ph.D. Thesis, University of BC, Vancouver, Canada (2008). [Google Scholar]
  19. W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer (2003). [Google Scholar]
  20. Y. Li and D.W. Oldenburg, Inversion of 3-D DC resistivity data using an approximate inverse mapping. Geophys. J. Int. 116 (1994) 557–569. [Google Scholar]
  21. J. Nagy and K. Palmer, Steepest descent, CG and iterative regularization of ill-posed problems. BIT 43 (2003) 1003–1017. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Nocedal and S. Wright, Numerical Optimization. Springer, New York (1999). [Google Scholar]
  23. J. Nocedal, A. Sartenar and C. Zhu, On the behavior of the gradient norm in the steepest descent method. Comput. Optim. Appl. 22 (2002) 5–35. [CrossRef] [MathSciNet] [Google Scholar]
  24. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer (2003). [Google Scholar]
  25. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629–639. [CrossRef] [Google Scholar]
  26. L. Pronzato, H. Wynn and A. Zhigljavsky, Dynamical Search: Applications of Dynamical Systems in Search and Optimization. Chapman & Hall/CRC, Boca Raton (2000). [Google Scholar]
  27. M. Raydan and B. Svaiter, Relaxed steepest descent and Cauchy-Barzilai-Borwein method. Comput. Optim. Appl. 21 (2002) 155–167. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Sincovec and N. Madsen, Software for nonlinear partial differential equations. ACM Trans. Math. Software 1 (1975) 232–260. [CrossRef] [Google Scholar]
  29. N.C. Smith and K. Vozoff, Two dimensional DC resistivity inversion for dipole dipole data. IEEE Trans. Geosci. Remote Sens. 22 (1984) 21–28. [CrossRef] [Google Scholar]
  30. G. Strang and G. Fix, An Analysis of the Finite Element Method. Prentice-Hall, Engelwood Cliffs, NJ (1973). [Google Scholar]
  31. E. Tadmor, S. Nezzar and L. Vese, A multiscale image representation using hierarchical (BV, L2) decompositions. SIAM J. Multiscale Model. Simul. 2 (2004) 554–579. [CrossRef] [Google Scholar]
  32. E. van den Berg and M. Friedlander, Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31 (2008) 840–912. [Google Scholar]
  33. K. van den Doel and U. Ascher, On level set regularization for highly ill-posed distributed parameter estimation problems. J. Comp. Phys. 216 (2006) 707–723. [CrossRef] [MathSciNet] [Google Scholar]
  34. K. van den Doel and U. Ascher, Dynamic level set regularization for large distributed parameter estimation problems. Inverse Problems 23 (2007) 1271–1288. [CrossRef] [MathSciNet] [Google Scholar]
  35. C. Vogel, Computational methods for inverse problem. SIAM, Philadelphia, USA (2002). [Google Scholar]
  36. J. Weickert, Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998). [Google Scholar]

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