Monte Carlo Complexity of Global Solution of Integral Equations
Monte Carlo Complexity of Global Solution of Integral Equations
复制标题
积分方程全局解的蒙特卡罗复杂度
DOI：
10.1006/jcom.1998.0471
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
S. Heinrich
中科院分区：
文献类型：
--
作者：
S. Heinrich
研究了Fredholm积分方程的全局解决方案的问题。这意味着人们试图近似完整的解决方案函数（与局部问题相反，只有单个点或解决方案功能中的解决方案的值才能寻求解决方案的值）。分析了蒙特卡洛的复杂性，即该问题的随机解的复杂性。该分析的框架由基于信息的复杂性理论提供。研究补充了先前关于局部解决方案的随机复杂性以及局部和全球解决方案的确定性复杂性的研究。结果表明，即使在全球情况下，蒙特卡洛算法也可以比确定性的算法更好，尽管差异不如当地情况。
The problem of the global solution of Fredholm integral equations is studied. This means that one seeks to approximate the full solution function (as opposed to the local problem, where only the value of the solution in a single point or a functional of the solution is sought). The Monte Carlo complexity, i.e., the complexity of the stochastic solution of this problem, is analyzed. The framework for this analysis is provided by information-based complexity theory. The investigations complement previous ones on the stochastic complexity of the local solution and on deterministic complexity of both local and global solutions. The results show that even in the global case Monte Carlo algorithms can perform better than deterministic ones, although the difference is not as large as in the local case.