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A Damped Newton Algorithm for Generated Jacobian Equations
arXiv - CS - Numerical Analysis Pub Date : 2021-01-20 , DOI: arxiv-2101.08080
Anatole GallouëtLJK, Quentin MerigotLMO, Boris ThibertLJK

Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Amp{\`e}re equations arising in optimal transport. In this paper, we introduce and study a damped Newton algorithm for solving these equations in the semi-discrete setting, meaning that one of the two measures involved in the problem is finitely supported and the other one is absolutely continuous. We also present a numerical application of this algorithm to the near-field parallel refractor problem arising in non-imaging problems.

中文翻译:

生成雅可比方程的牛顿阻尼算法

生成的雅可比方程式已由Trudinger [Disc。续 达因 sys(2014),pp。1663-1681]作为在最优输运中产生的Monge-Amp {\ e} re方程的推广。在本文中,我们引入并研究了一种阻尼牛顿算法,用于在半离散环境中求解这些方程,这意味着该问题所涉及的两个度量之一是有限支持的,另一个是绝对连续的。我们还提出了该算法在非成像问题中引起的近场平行折射问题上的数值应用。
更新日期:2021-01-21
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