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A link between the steepest descent method and fixed-point iterations
We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler–Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the co...
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| Formato: | Online Artículo Texto |
| Lenguaje: | English |
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Springer Berlin Heidelberg
2022
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| Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9813030/ https://www.ncbi.nlm.nih.gov/pubmed/36619368 http://dx.doi.org/10.1007/s11590-022-01867-9 |
| Sumario: | We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler–Lagrange equation. In this context, we shall rediscover the preconditioned algebraic conjugate gradient method for the discretised problem. The benefit of the connection of those concepts will be illustrated by a numerical experiment. |
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