用于计算一般图适应度中心性的非线性不动点迭代的收敛性与加速
Convergence and acceleration of a nonlinear fixed-point iteration for computing the Fitness Centrality of general graphs
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中文总结 AI 辅助
该研究针对一般图的适应度中心性计算，证明了对应非线性不动点迭代的全局收敛性与显式收敛界，并通过Anderson加速和牛顿切换策略提升收敛速度，数值实验验证了其有效性。
中文摘要 AI 辅助
我们建立了适用于一般图的（非齐次）适应度中心性算法的全局收敛性，推导了对应不动点迭代的显式收敛界。此外，我们展示了如何通过Anderson加速法，以及在找到足够好的不动点近似后切换为牛顿法，来大幅提升收敛速度。不同类型图的数值实验证明了该策略的有效性。
英文摘要
We establish the global convergence of the (non-homogeneous) Fitness Centrality algorithm for general graphs, deriving an explicit convergence bound for the corresponding fixed-point iteration. Furthermore, we show how the convergence can be dramatically improved by Anderson acceleration and by switching to Newton's method once a sufficiently good approximation to the fixed point has been found. The efficacy of this strategy is illustrated by numerical experiments on different types of graphs.
发表机构
- Faculty of Sciences, Scuola Normale Superiore（高等师范学校理学院）
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