Dual Numbers for Algorithmic Differentiation
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Redalyc
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Universidad Autónoma de Yucatán
2019
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| _version_ | 1876481164433162240 |
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| author | F. Peñuñuri |
| author_facet | F. Peñuñuri |
| contents | Dual Numbers for Algorithmic Differentiation F. Peñuñuri O. Carvente M.A. Zambrano-Arjona R. Peón Carlos A. Cruz-Villar Computación Runge Newton Dual numbers Differentiation Kutta algorithm The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Matlab and some examples are presented. Among them, we use the dual Newton–Raphson method to obtain the derivatives of the output angle in the RRRCR spatial mechanism; we use the dual normal cubic spline interpolation algorithm to obtain the thermal diffusivity using photothermal techniques; and we use the dual Runge–Kutta method to obtain the derivatives of functions depending on the solution of the Duffing equation. 2019 artículo científico 1665-529X https://www.redalyc.org/articulo.oa?id=46761359006 https://www.redalyc.org/journal/467/46761359006/ https://www.redalyc.org/journal/467/46761359006/html/ https://www.redalyc.org/journal/467/46761359006/46761359006.epub https://www.redalyc.org/journal/467/46761359006/movil en http://www.redalyc.org/revista.oa?id=467 Ingeniería application/pdf Universidad Autónoma de Yucatán Ingeniería (México) Num.3 Vol.23 |
| format | Artículo científico |
| id | redalyc_46761359006 |
| institution | Redalyc |
| language | en |
| publishDate | 2019 |
| publisher | Universidad Autónoma de Yucatán |
| spellingShingle | Dual Numbers for Algorithmic Differentiation F. Peñuñuri Computación Runge Newton Dual numbers Differentiation Kutta algorithm Dual Numbers for Algorithmic Differentiation F. Peñuñuri O. Carvente M.A. Zambrano-Arjona R. Peón Carlos A. Cruz-Villar Computación Runge Newton Dual numbers Differentiation Kutta algorithm The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Matlab and some examples are presented. Among them, we use the dual Newton–Raphson method to obtain the derivatives of the output angle in the RRRCR spatial mechanism; we use the dual normal cubic spline interpolation algorithm to obtain the thermal diffusivity using photothermal techniques; and we use the dual Runge–Kutta method to obtain the derivatives of functions depending on the solution of the Duffing equation. 2019 artículo científico 1665-529X https://www.redalyc.org/articulo.oa?id=46761359006 https://www.redalyc.org/journal/467/46761359006/ https://www.redalyc.org/journal/467/46761359006/html/ https://www.redalyc.org/journal/467/46761359006/46761359006.epub https://www.redalyc.org/journal/467/46761359006/movil en http://www.redalyc.org/revista.oa?id=467 Ingeniería application/pdf Universidad Autónoma de Yucatán Ingeniería (México) Num.3 Vol.23 |
| title | Dual Numbers for Algorithmic Differentiation |
| topic | Computación Runge Newton Dual numbers Differentiation Kutta algorithm |
| url | https://www.redalyc.org/articulo.oa?id=46761359006 https://www.redalyc.org/journal/467/46761359006/ https://www.redalyc.org/journal/467/46761359006/html/ https://www.redalyc.org/journal/467/46761359006/46761359006.epub https://www.redalyc.org/journal/467/46761359006/movil |