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 for more details. If you have signed a license agreement for commercial use, then you may download the complete NewtonLib as one compressed tar-file here.
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:
- GMRES - Generalized minimal residual method; residuum norm based termination criterion (Section 1.4.1)
Source code gmres.c | Download directory | Tar file - PCG - adaptive preconditioned conjugate gradient method for linear systems with symmetric positive definite matrix; energy error norm based termination criterion (Section 1.4.2)
Source code pcg.c | Download directory | Tar file - GBIT - adaptive Broyden's 'good' rank-1 update method specialized for linear equations; error oriented termination criterion (Section 1.4.4)
New C source code gbit.c | Download directory | Tar file
Old Fortran source code gbit1.f | Download directory | Tar file
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, full or banded Jacobian
Source code nleq1.f | Download directory | Fortran code tar file | Matlab source nleq1.m | Matlab code download directory | Matlab code tar file - NLEQ1S - same algorithm as NLEQ1, sparse Jacobian
Source code nleq1s.f | Download directory | Tar file - 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:
- QNERR - recursive implementation of Broyden's 'good' rank-1 update method; error oriented convergence criterion (Section 2.1.4)
Source code qnerr.c | Download directory | Tar file - QNRES - recursive implementation of Broyden's 'bad' rank-1 update method; residual based convergence criterion (Section 2.2.3)
Source code qnres.c | Download directory | Tar file
Continuation methods for parameter dependent systems of nonlinear equations:
- ALCON1 - global quasi-Gauss-Newton continuation method; adaptive path-following beyond turning points (Section 5.2.3)
Source code alcon1.f | Download directory | Tar file - ALCON2 - global quasi-Gauss-Newton continuation method; adaptive path-following beyond turning points; computation of bifurcation diagrams including simple bifurcations (Sections 5.2.3, 5.3.2, and 5.3.3)
Source code alcon2.f | Download directory | Tar file - ALCON-S - Pathfollowing method for sparse parameter-dependent nonlinear systems of equations. Includes several application examples.
more information | Download directory | Tar file
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 | Fortran code tar file | Matlab source nlscon.m | Matlab code download directory | Matlab code tar file - 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)
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Last update: Fri Jul 07 2017