Complexity of the contraction mappingprinciple with noises

• Main Authors: Ying-Chi Lin, 林英期
• Other Authors: Ching-Lueh Chang
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/37589268269831562102

碩士 === 元智大學 === 資訊工程學系 === 102 === A function f:M→M is called a contraction mapping on a metric space (M,d) if there exists ρ∈(0,1) satisfying d(f(x),f(y) )≤ρd(x,y) for all x,y∈M. The celebrated contraction mapping principle states that each contraction mapping on a complete metric space has a unique fixed point. Chang and Lyuu [1] propose a randomized algorithm that, given oracle access to a finite metric space (M,d) and a contraction mapping f on it, outputs the fixed point of f after making an expected number of O(√(|M| )) queries. To complement their result, we show that any randomized algorithm must have an expected query complexity of Ω(|M| ) if the distance queries have small yet arbitrary noises.