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Numerical Analysis and Modelling - NewtonLib

Software repository for Peter Deuflhards Book
“Newton Methods for Nonlinear Problems -- Affine Invariance and Adaptive Algorithms”


This monograph presents a scheme to construct adaptive Newton-type algorithms in close connection with an associated affine invariant convergence analysis. Part of these algorithms are presented as informal programs in the text. Some, but not all of the described algorithms have been worked out in detail. Below follows a list of codes mentioned by name in the book.

All of the available programs (not only by the author and his group) are free as long as they are exclusively used for research or teaching purposes. For commercial use of the software you must sign a license-agreement with the ZIB and pay a license-charge that depends on the referenced software package and the intended usage. Please read our sample license agreement (or the german version) for more details.

An asterisks * indicate that a code is still under development at the time of the appearance of the book in print.

Iterative methods for large systems of linear equations:

Exact global Newton methods for systems of nonlinear equations:

  • NLEQ1 - popular production code; global Newton method with error oriented convergence criterion; arbitrary selection of direct linear equation solver; adaptive damping strategies slightly different from Section 3.3.3; no rank strategy
    Source code nleq1.f  Download directory  Tar file  Matlab source nleq1.m
  • NLEQ2 - production code; global Newton method with error oriented convergence criterion; QR-decomposition with subcondition number estimate; adaptive damping and rank strategy slightly different from Section 3.3.3
    Source code nleq2.f  Download directory  Tar file
  • NLEQ_RES - global Newton method with residual based convergence criterion and adaptive trust region strategy (Section 3.2.2)
    Source code nleq_res.c  Download directory  Tar file
  • NLEQ_ERR - global Newton method with error oriented convergence criterion and adaptive trust region strategy (Section 3.3.3)
    Source code nleq_err.c  Download directory  Tar file
  • NLEQ-OPT - global Newton method for gradient systems originating from convex optimization; energy error norm oriented or objective function based convergence criteria and adaptive trust region strategy (Section 3.4.2)

Local quasi-Newton methods for systems of nonlinear equations:

Continuation methods for parameter dependent systems of nonlinear equations:

Global Gauss-Newton methods for nonlinear least squares problems:

  • NLSCON - (older) global constrained (or unconstrained) Gauss-Newton method with error oriented convergence criterion; adaptive trust region strategies slightly different from Sections 4.3.4 and 4.1.2
    Source code nlscon.f  Download directory  Tar file  Matlab source nlscon.m
  • NLSQ_RES* - global unconstrained Gauss-Newton method with projected residual based convergence criterion and adaptive trust region strategy (Section 4.2.3)
    Download directory  Tar file
  • NLSQ_ERR* - global unconstrained Gauss-Newton method with error oriented convergence criterion and adaptive trust region strategies (Sections 4.3.4 and 4.3.5)
    Download directory  Tar file

Inexact global Newton methods for large systems of nonlinear equations:

  • GIANT - (older) global inexact Newton method with error oriented convergence criterion; adaptive trust region strategy slightly different from Sections 2.1.5 and 3.3.4; earlier version of GBIT for inner iteration
    Source code giant.f  Download directory  Tar file
  • GIANT-GMRES* - global inexact Newton method with residual based convergence criterion and adaptive trust region strategy; GMRES for inner iteration (Sections 2.2.4 and 3.2.3)
    Source code giant-gmres.c  Download directory  Tar file
  • GIANT-GBIT* - global inexact Newton method with error oriented convergence criterion and adaptive trust region strategy; GBIT for inner iteration (Sections 2.1.5 and 3.3.4)
    Source code giant-gbit.c  Download directory  Tar file
  • GIANT-PCG - global inexact Newton method for gradient systems originating from convex function optimization; energy error norm oriented or function based convergence criteria and adaptive trust region strategy; PCG for inner iteration (Sections 2.3.3 and 3.4.3)

Multiple shooting methods for ODE boundary value problems:

  • BVPSOL - Multiple shooting method for two-point boundary value problems; exact global Newton method with error oriented convergence criterion and adaptive trust region strategies (Section 7.1.2)
    Source code bvpsol.f  Download directory  Tar file
  • MULCON - Multiple shooting method for two-point boundary value problems; adaptive Gauss-Newton continuation method (Section 7.1.3)
    Source code mulcon.f  Download directory  Tar file
  • PERIOD - multiple shooting method for periodic solutions of ODEs; global underdetermined Gauss-Newton method with error oriented convergence criterion and adaptive trust region strategies (Section 7.3.1)
    Source code period.f  Download directory  Tar file
  • PERHOM - multiple shooting method for periodic solutions of parameter dependent ODEs; adaptive error oriented underdetermined Gauss-Newton orbit continuation method (Section 7.3.2)
    Source code perhom.f  Download directory  Tar file
  • PARKIN - single shooting method for parameter identification in large reaction kinetic ODE networks; global Gauss-Newton method with error oriented convergence measure and adaptive trust region strategies (Section 7.2)

Adaptive multilevel finite element methods for elliptic PDEs:

  • Newton-KASKADE* - function space oriented global inexact Newton multilevel FEM for nonlinear elliptic PDEs originating from convex optimization; energy error norm oriented or objective functional based convergence criteria and adaptive trust region strategy; adaptive multilevel code KASKADE for inner iteration (Section 8.3)