EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 6 (November-December 2021) ESAIM: M2AN, 55 6 (2021) 2785-2825 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
Page(s) 2785 - 2825
DOI https://doi.org/10.1051/m2an/2021069
Published online 25 November 2021
  1. H. An, X. Jia and H.F. Walker, Anderson acceleration and application to the three-temperature energy equations. J. Comput. Phys. 347 (2017) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Anantharaman and E. Cancès, Existence of minimizers for Kohn-Sham models in quantum chemistry. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2425–2455. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.G. Anderson, Iterative procedures for nonlinear integral equations. J. ACM 12 (1965) 547–560. [CrossRef] [Google Scholar]
  4. D.G.M. Anderson, Comments on ``Anderson acceleration, mixing and extrapolation’’. Numer. Algorithms 80 (2019) 135–234. [CrossRef] [MathSciNet] [Google Scholar]
  5. A.S. Banerjee, P. Suryanarayana and J.E. Pask, Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations. Chem. Phys. Lett. 647 (2016) 31–35. [CrossRef] [Google Scholar]
  6. A.D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38 (1988) 3098–3100. [NASA ADS] [CrossRef] [Google Scholar]
  7. C. Brezinski, M. Redivo-Zaglia and Y. Saad, Shanks sequence transformations and Anderson acceleration. SIAM Rev. 60 (2018) 646–669. [CrossRef] [MathSciNet] [Google Scholar]
  8. C.G. Broyden, A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19 (1965) 577–593. [CrossRef] [Google Scholar]
  9. M.T. Calef, E.D. Fichtl, J.S. Warsa, M. Berndt and N.N. Carlson, Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem. J. Comput. Phys. 238 (2013) 188–209. [CrossRef] [MathSciNet] [Google Scholar]
  10. E. Cancès and C. Le Bris, Can we outperform the DIIS approach for electronic structure calculations?. Int. J. Quantum Chem. 79 (2000) 82–90. [CrossRef] [Google Scholar]
  11. E. Cancès and C. Le Bris, On the convergence of SCF algorithms for the Hartree-Fock equations. ESAIM: M2AN 34 (2000) 749–774. [CrossRef] [EDP Sciences] [Google Scholar]
  12. N.N. Carlson and K. Miller, Design and application of a gradient-weighted moving finite element code I: in one dimension. SIAM J. Sci. Comput. 19 (1998) 728–765. [CrossRef] [MathSciNet] [Google Scholar]
  13. X. Chen and C.T. Kelley, Convergence of the EDIIS algorithm for nonlinear equations. SIAM J. Sci. Comput. 41 (2019) A365–A379. [CrossRef] [Google Scholar]
  14. P. Császár and P. Pulay, Geometry optimization by direct inversion in the iterative subspace. J. Mol. Struct. 114 (1984) 31–34. [CrossRef] [Google Scholar]
  15. H. De Sterck, A nonlinear GMRES optimization algorithm for canonical tensor decomposition. SIAM J. Sci. Comput. 34 (2012) A1351–A1379. [CrossRef] [Google Scholar]
  16. E. De Sturler, Truncation strategies for optimal Krylov subspace methods. SIAM J. Numer. Anal. 36 (1999) 864–889. [CrossRef] [MathSciNet] [Google Scholar]
  17. V. Eckert, P. Pulay and H.-J. Werner, Ab initio geometry optimization for large molecules. J. Comput. Chem. 18 (1997) 1473–1483. [CrossRef] [Google Scholar]
  18. C. Evans, S. Pollock, L.G. Rebholz and M. Xiao, A proof that Anderson acceleration increases the convergence rate in linearly converging fixed point methods (but not in quadratically converging ones). SIAM J. Numer. Anal. 58 (2020) 788–810. [CrossRef] [MathSciNet] [Google Scholar]
  19. V. Eyert, A comparative study on methods for convergence acceleration of iterative vector sequences. J. Comput. Phys. 124 (1996) 271–285. [CrossRef] [MathSciNet] [Google Scholar]
  20. H.-R. Fang and Y. Saad, Two classes of multisecant methods for nonlinear acceleration. Numer. Linear Algebra Appl. 16 (2009) 197–221. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.-L. Fattebert, Accelerated block preconditioned gradient method for large scale wave functions calculations in density functional theory. J. Comput. Phys. 229 (2010) 441–452. [CrossRef] [MathSciNet] [Google Scholar]
  22. V. Fock, Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys. 61 (1930) 126–148. [CrossRef] [Google Scholar]
  23. V. Ganine, N.J. Hills and B.L. Lapworth, Nonlinear acceleration of coupled fluid-structure transient thermal problems by Anderson mixing. Int. J. Numer. Methods Fluids 71 (2013) 939–959. [CrossRef] [Google Scholar]
  24. A.J. Garza and G.E. Scuseria, Comparison of self-consistent field convergence acceleration techniques. J. Chem. Phys. 137 (2012) 054110. [CrossRef] [PubMed] [Google Scholar]
  25. D.M. Gay and R.B. Schnabel, Solving systems of nonlinear equations by Broyden’s method with projected updates. Working Paper 169, National Bureau of Economic Research (1977). [CrossRef] [Google Scholar]
  26. A. Greenbaum, V. Pták and Z. Strakoš, Any nonincreasing convergence curve is possible for GMRES. SIAM. J. Matrix Anal. Appl. 17 (1996) 465–469. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Griewank, Broyden updating, the good and the bad! Documenta Math. Extra Volume: Optimization Stories. (2012) 301–315. [Google Scholar]
  28. R. Haelterman, J. Degroote, D. Van Heule and J. Vierendeels, On the similarities between the quasi-Newton inverse least squares method and GMRES. SIAM J. Numer. Anal. 47 (2010) 4660–4679. [CrossRef] [MathSciNet] [Google Scholar]
  29. G.G. Hall, The molecular orbital theory of chemical valency. VIII. A method of calculating ionization potentials. Proc. Roy. Soc. London Ser. A 205 (1951) 541–552. [Google Scholar]
  30. D.R. Hartree, The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods. Math. Proc. Cambridge Philos. Soc. 24 (1928) 89–110. [CrossRef] [Google Scholar]
  31. N.C. Henderson and R. Varadhan, Damped Anderson acceleration with restarts and monotonicity control for accelerating EM and EM-like algorithms. J. Comput. Graph. Stat. 28 (2019) 834–846. [CrossRef] [Google Scholar]
  32. N.J. Higham and N. Strabić, Anderson acceleration of the alternating projections method for computing the nearest correlation matrix. Numer. Algorithms 72 (2016) 1021–1042. [CrossRef] [MathSciNet] [Google Scholar]
  33. P. Hohenberg and W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136 (1964) B864–B871. [CrossRef] [Google Scholar]
  34. X. Hu and W. Yang, Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function. J. Chem. Phys. 132 (2010) 054109. [CrossRef] [PubMed] [Google Scholar]
  35. M. Kawata, C.M. Cortis and R.A. Friesner, Efficient recursive implementation of the modified Broyden method and the direct inversion in the iterative subspace method: acceleration of self-consistent calculations. J. Chem. Phys. 108 (1998) 4426–4438. [CrossRef] [Google Scholar]
  36. W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133–A1138. [CrossRef] [Google Scholar]
  37. K.N. Kudin and G.E. Scuseria, Converging self-consistent field equations in quantum chemistry – Recent achievements and remaining challenges. ESAIM: M2AN 41 (2007) 281–296. [CrossRef] [EDP Sciences] [Google Scholar]
  38. K.N. Kudin, G.E. Scuseria and E. Cancès, A black-box self-consistent field convergence algorithm: one step closer. J. Chem. Phys. 116 (2002) 8255–8261. [CrossRef] [Google Scholar]
  39. C. Lee, W. Yang and R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37 (1988) 785–789. [Google Scholar]
  40. P.A. Lott, H.F. Walker, C.S. Woodward and U.M. Yang, An accelerated Picard method for nonlinear systems related to variably saturated flow. Adv. Water Res. 38 (2012) 92–101. [CrossRef] [Google Scholar]
  41. J. Nocedal and S.J. Wright, Numerical Optimization, 2nd edition. Springer Series in Operations Research and Financial Engineering. Springer-Verlag, New York (2006). [Google Scholar]
  42. A.L. Pavlov, G.W. Ovchinnikov, D.Y. Derbyshev, D. Tsetserukou and I.V. Oseledets, AA-ICP: iterative closest point with Anderson acceleration. In: 2018 IEEE International Conference on Robotics and Automation (ICRA) (2018) 3407–3412. [Google Scholar]
  43. F.A. Potra, On Q-order and R-order of convergence. J. Optim. Theory Appl. 63 (1989) 415–431. [CrossRef] [MathSciNet] [Google Scholar]
  44. F.A. Potra and H. Engler, A characterization of the behavior of the Anderson acceleration on linear problems. Linear Algebra Appl. 438 (2013) 393–398. [Google Scholar]
  45. P.P. Pratapa and P. Suryanarayana, Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations. Chem. Phys. Lett. 635 (2015) 69–74. [CrossRef] [Google Scholar]
  46. P. Pulay, Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73 (1980) 393–398. [CrossRef] [Google Scholar]
  47. P. Pulay, Improved SCF convergence acceleration. J. Comput. Chem. 3 (1982) 556–560. [CrossRef] [Google Scholar]
  48. T. Rohwedder and R. Schneider, An analysis for the DIIS acceleration method used in quantum chemistry calculations. J. Math. Chem. 49 (2011) 1889–1914. [CrossRef] [MathSciNet] [Google Scholar]
  49. C.C.J. Roothaan, New developments in molecular orbital theory. Rev. Modern Phys. 23 (1951) 69–89. [CrossRef] [Google Scholar]
  50. Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 (1986) 856–869. [CrossRef] [MathSciNet] [Google Scholar]
  51. H. Sellers, The C2-DIIS convergence acceleration algorithm. Int. J. Quantum Chem. 45 (1993) 31–41. [CrossRef] [Google Scholar]
  52. H. Shepard and M. Minkoff, Some comments on the DIIS method. Mol. Phys. 105 (2007) 2839–2848. [CrossRef] [Google Scholar]
  53. M. Spivak, A Comprehensive Introduction to Differential Geometry, 3rd edition. Vol. 1. Publish or Perish (1999). [Google Scholar]
  54. Q. Sun, T.C. Berkelbach, N.S. Blunt, G.H. Booth, S. Guo, Z. Li, J. Liu, J.D. McClain, E.R. Sayfutyarova, S. Sharma, S. Wouters and G.K. Chan, PySCF: the Python-based simulations of chemistry framework. WIREs Comput. Mol. Sci. 8 (2017) e1340. [Google Scholar]
  55. L. Thøgersen, J. Olsen, A. Köhn, P. Jørgensen, P. Sałek and T. Helgaker, The trust-region self-consistent field method in Kohn-Sham density-functional theory. J. Chem. Phys. 123 (2005) 074103. [CrossRef] [PubMed] [Google Scholar]
  56. A. Toth and C.T. Kelley, Convergence analysis for Anderson acceleration. SIAM J. Numer. Anal. 53 (2015) 805–819. [CrossRef] [MathSciNet] [Google Scholar]
  57. A. Toth, J.A. Ellis, T. Evans, S. Hamilton, C.T. Kelley, R. Pawlowski and S. Slattery, Local improvement results for Anderson acceleration with inaccurate function evaluations. SIAM J. Sci. Comput. 39 (2017) S47–S65. [CrossRef] [Google Scholar]
  58. H.F. Walker and P. Ni, Anderson acceleration for fixed-point iterations. SIAM J. Numer. Anal. 49 (2011) 1715–1735. [CrossRef] [MathSciNet] [Google Scholar]
  59. Y.A. Wang, C.Y. Yam, Y.K. Chen and G. Chen, Linear-expansion shooting techniques for accelerating self-consistent field convergence. J. Chem. Phys. 134 (2011) 241103. [CrossRef] [PubMed] [Google Scholar]
  60. T. Washio and C.W. Oosterlee, Krylov subspace acceleration for nonlinear multigrid schemes. Electron. Trans. Numer. Anal. 6 (1997) 271–290. [MathSciNet] [Google Scholar]
  61. J. Willert, W.T. Taitano and D. Knoll, Leveraging Anderson acceleration for improved convergence of iterative solutions to transport systems. J. Comput. Phys. 273 (2014) 278–286. [CrossRef] [Google Scholar]
  62. D.M. Wood and A. Zunger, A new method for diagonalising large matrices. J. Phys. A Math. Gen. 18 (1985) 1343–1359. [CrossRef] [Google Scholar]
  63. Y.A. Zhang and Y.A. Wang, Perturbative total energy evaluation in self-consistent field iterations: tests on molecular systems. J. Chem. Phys. 130 (2009) 144116. [CrossRef] [PubMed] [Google Scholar]
  64. J. Zhang, Y. Yao, Y. Peng, H. Yu and B. Deng, Fast K-Means clustering with Anderson acceleration. Preprint arXiv:1805.10638 [cs.LG] (2018). [Google Scholar]
  65. J. Zhang, B. O’Donoghue and S. Boyd, Globally convergent type-I Anderson acceleration for non-smooth fixed-point iterations. SIAM J. Optim. 30 (2020) 3170–3197. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you