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.

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  1. Liu, Lulu; Keyes, David E.: Convergence analysis for the multiplicative Schwarz preconditioned inexact Newton algorithm (2016)
  2. Gaul, André; Schlömer, Nico: Preconditioned recycling Krylov subspace methods for self-adjoint problems (2015)
  3. Liu, Lulu; Keyes, David E.: Field-split preconditioned inexact Newton algorithms (2015)
  4. Rahul; De, Suvranu: Analysis of the Jacobian-free multiscale method (JFMM) (2015)
  5. Alizard, Frédéric; Robinet, Jean-Christophe; Guiho, Florian: Transient growth in a right-angled streamwise corner (2013)
  6. Newman, C.; Knoll, D.A.: Physics-based preconditioners for ocean simulation (2013)
  7. Ahmed, Sarfraz; Goodyer, Christopher E.; Jimack, Peter K.: An efficient preconditioned iterative solution of fully-coupled elastohydrodynamic lubrication problems (2012)
  8. Godoy, William F.; Liu, Xu: Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer (2012)
  9. Jardin, S.C.: Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas (2012)
  10. Yang, Ai-Li; Wu, Yu-Jiang: Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices (2012)
  11. An, Heng-Bin; Wen, Ju; Feng, Tao: On finite difference approximation of a matrix-vector product in the Jacobian-free Newton-Krylov method (2011)
  12. Bellavia, Stefania; Bertaccini, Daniele; Morini, Benedetta: Nonsymmetric preconditioner updates in Newton-Krylov methods for nonlinear systems (2011)
  13. Bellavia, Stefania; De Simone, Valentina; di Serafino, Daniela; Morini, Benedetta: Efficient preconditioner updates for shifted linear systems (2011)
  14. Cai, Xiao-Chuan; Li, Xuefeng: Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity (2011)
  15. Crivellini, A.; Bassi, F.: An implicit matrix-free discontinuous Galerkin solver for viscous and turbulent aerodynamic simulations (2011)
  16. Deuflhard, Peter: Newton methods for nonlinear problems. Affine invariance and adaptive algorithms. (2011)
  17. Hansen, Glen: A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems (2011)
  18. Morrow, W.Ross; Skerlos, Steven J.: Fixed-point approaches to computing Bertrand-Nash equilibrium prices under mixed-logit demand (2011)
  19. Alizard, Frédéric; Robinet, Jean-Christophe; Rist, Ulrich: Sensitivity analysis of a streamwise corner flow (2010)
  20. Bailey, David; Berndt, Markus; Kucharik, Milan; Shashkov, Mikhail: Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods (2010)

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