# Numerical Mathematics- 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 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:

Exact global Newton methods for systems of nonlinear equations:

Local quasi-Newton methods for systems of nonlinear equations:

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)
• 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)
• ALCON-S - Pathfollowing method for sparse parameter-dependent nonlinear systems of equations. Includes several application examples.
• Global Gauss-Newton methods for nonlinear least squares problems:

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