We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods. The algorithm is implemented in a Fortran solver called NITSOL that is robust yet easy to use and provides a number of useful options and features. The structure offers the user great flexibility in addressing problem specificity through preconditioning and other means and allows easy adaptation to parallel environments. Features and capabilities are illustrated in numerical experiments.

References in zbMATH (referenced in 97 articles , 1 standard article )

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  1. Crivellini, A.; Bassi, F.: An implicit matrix-free discontinuous Galerkin solver for viscous and turbulent aerodynamic simulations (2011)
  2. Deuflhard, Peter: Newton methods for nonlinear problems. Affine invariance and adaptive algorithms. (2011)
  3. Guo, Xue-Ping; Duff, Iain S.: Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations. (2011)
  4. Hansen, Glen: A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems (2011)
  5. Morrow, W. Ross; Skerlos, Steven J.: Fixed-point approaches to computing Bertrand-Nash equilibrium prices under mixed-logit demand (2011)
  6. Alizard, Frédéric; Robinet, Jean-Christophe; Rist, Ulrich: Sensitivity analysis of a streamwise corner flow (2010)
  7. Bailey, David; Berndt, Markus; Kucharik, Milan; Shashkov, Mikhail: Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods (2010)
  8. Lütjens, Hinrich; Luciani, Jean-François: XTOR-2F: a fully implicit Newton-Krylov solver applied to nonlinear 3D extended MHD in tokamaks (2010)
  9. Pashos, George; Koronaki, Eleni D.; Spyropoulos, Antony N.; Boudouvis, Andreas G.: Accelerating an inexact Newton/GMRES scheme by subspace decomposition (2010)
  10. Tromeur-Dervout, Damien; Vassilevski, Yuri: Acceleration of iterative solution of series of systems due to better initial guess (2010)
  11. Alizard, Frédéric; Cherubini, Stefania; Robinet, Jean-Christophe: Sensitivity and optimal forcing response in separated boundary layer flows (2009)
  12. Fang, Liang; He, Guoping: Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations (2009)
  13. Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan: Algorithm 896: LSA: algorithms for large-scale optimization (2009)
  14. Pacull, F.; Garbey, M.: On the Fourier representation of elastic immersed boundaries (2009)
  15. Park, Hyeongkae; Nourgaliev, Robert R.; Martineau, Richard C.; Knoll, Dana A.: On physics-based preconditioning of the Navier-Stokes equations (2009)
  16. Wilkins, A. Katharina; Tidor, Bruce; White, Jacob; Barton, Paul I.: Sensitivity analysis for oscillating dynamical systems (2009)
  17. An, Heng-Bin; Mo, Ze-Yao; Xu, Xiao-Wen; Liu, Xu: On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations (2008)
  18. Berndt, Markus; Moulton, J. David; Hansen, Glen: Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids (2008)
  19. Gomes-Ruggiero, Márcia A.; Lopes, Véra Lucia Rocha; Toledo-Benavides, Julia Victoria: A globally convergent inexact Newton method with a new choice for the forcing term (2008)
  20. Spiteri, Raymond J.; Ter, Thian-Peng: pythNon: A PSE for the numerical solution of nonlinear algebraic equations (2008)