 |
|
|
|
|
 |
 |
|
Extended Newton-Raphson's Method
|
|
|
|
|
|
| Organization: | Budapest University of Technology and Economics |
| Department: | Photogrammetry and Geoinformatics |
|
|
|
|
|
|
2008-02-05
|
|
|
|
|
|
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.
|
|
|
|
|
|
|
|
|
|
|
|
Newton-Raphson method, over and under determined nonlinear systems, singular Jacobian, pseudoinverse, singular value decomposition
|
|
|
 |
|
|
| ExtendedNewton.nb (210.6 KB) - Mathematica Notebook |
|
|
For the newest resources, visit Wolfram Repositories and Archives »
