一种基于对角化的抛物型最优控制问题的预处理子
A Preconditioner for Parabolic Optimal Control Problems Based on Diagonalization
DOI: 10.12677/aam.2024.135241, PDF,   
作者: 高 广：中国地质大学(武汉)，数学与物理学院，湖北 武汉
关键词: 预处理子；最优控制；抛物方程；对角化；Preconditioner； Optimal Control； Parabolic Equations； Diagonalization
摘要: 本文研究了求解抛物型偏微分方程约束的最优控制问题，利用对角化技巧，提出了一个新的基于对角化的预处理子，用于快速求解大型稀疏方程组。数值实验说明了预处理子的良好加速效果和稳定性。
Abstract: In this paper, we study the solution of the optimal control problem constrained by parabolic partial differential equations. By using the diagonalization technique, we propose a new preconditioner based on diagonalization to quickly calculate the large sparse equation system. Numerical experiments demonstrate the good acceleration effect and stability of the preconditioner.
文章引用：高广. 一种基于对角化的抛物型最优控制问题的预处理子[J]. 应用数学进展, 2024, 13(5): 2530-2540. https://doi.org/10.12677/aam.2024.135241

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