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Extended Newton-Raphson's Method
Author

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Revision date

2008-02-05
Description

The standard Newton-Raphson's method has been extended for under and overdetermined systems or in more general, for situations when the Jacobian is not regular, has deficient rank, singular or ill-conditioned. Instead of using inverse of the Jacobian, its pseudoinverse computed by singular value decomposition is employed. The method implemented in Mathematica is fast and robust concerning the starting value of the iteration procedure and it can also restore quadratic convergence at multiple roots. The efficiency of the method is illustrated via many examples.
Subject

*Applied Mathematics > Numerical Methods
Keywords

Newton-Raphson method, over and under determined nonlinear systems, singular Jacobian, pseudoinverse, singular value decomposition
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ExtendedNewton.nb (210.6 KB) - Mathematica Notebook