Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded paramete...
| Authors: | , , , , , |
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| Format: | article |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/100357 |
| Online Access: | https://hdl.handle.net/2117/100357 https://dx.doi.org/10.3390/a9010018 |
| Access Level: | Open access |
| Keyword: | Iterative methods (Mathematics) systems of nonlinear equations frozen Jacobian ordinary differential equations partial differential equations homotopy method DIFFERENTIAL-EQUATIONS DECOMPOSITION METHOD NUMERICAL-SOLUTION NEWTONS METHOD Mètodes iteratius (Matemàtica) Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica |
| Summary: | A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations. |
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