SIR—An efficient solver for systems of equations
The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. We here present MATLAB and MAPLE codes for SIR, that can be easily implemented in any application where linear or nonlinear systems of equations need be solved efficiently....
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Elsevier
2018-01-01
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| Series: | SoftwareX |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2352711018300062 |
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doaj-83c1f3de35e545e386291ce3f12b78bd2020-11-24T21:50:06ZengElsevierSoftwareX2352-71102018-01-0175962SIR—An efficient solver for systems of equationsJan Scheffel0Kristoffer Lindvall1Department of Fusion Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, SwedenCorresponding author.; Department of Fusion Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, SwedenThe Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. We here present MATLAB and MAPLE codes for SIR, that can be easily implemented in any application where linear or nonlinear systems of equations need be solved efficiently. The codes employ recently developed efficient sparse matrix algorithms and improved numerical differentiation. SIR convergence is quasi-monotonous and approaches second order in the proximity of the real roots. Global convergence is usually superior to that of Newton’s method, being a special case of the method. Furthermore the algorithm cannot land on local minima, as may be the case for Newton’s method with line search. Keywords: Newton method, Root solver, Equation solver, MATLABhttp://www.sciencedirect.com/science/article/pii/S2352711018300062 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jan Scheffel Kristoffer Lindvall |
| spellingShingle |
Jan Scheffel Kristoffer Lindvall SIR—An efficient solver for systems of equations SoftwareX |
| author_facet |
Jan Scheffel Kristoffer Lindvall |
| author_sort |
Jan Scheffel |
| title |
SIR—An efficient solver for systems of equations |
| title_short |
SIR—An efficient solver for systems of equations |
| title_full |
SIR—An efficient solver for systems of equations |
| title_fullStr |
SIR—An efficient solver for systems of equations |
| title_full_unstemmed |
SIR—An efficient solver for systems of equations |
| title_sort |
sir—an efficient solver for systems of equations |
| publisher |
Elsevier |
| series |
SoftwareX |
| issn |
2352-7110 |
| publishDate |
2018-01-01 |
| description |
The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. We here present MATLAB and MAPLE codes for SIR, that can be easily implemented in any application where linear or nonlinear systems of equations need be solved efficiently. The codes employ recently developed efficient sparse matrix algorithms and improved numerical differentiation. SIR convergence is quasi-monotonous and approaches second order in the proximity of the real roots. Global convergence is usually superior to that of Newton’s method, being a special case of the method. Furthermore the algorithm cannot land on local minima, as may be the case for Newton’s method with line search. Keywords: Newton method, Root solver, Equation solver, MATLAB |
| url |
http://www.sciencedirect.com/science/article/pii/S2352711018300062 |
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AT janscheffel siranefficientsolverforsystemsofequations AT kristofferlindvall siranefficientsolverforsystemsofequations |
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