Solving discrete zero point problems

• 成果类型: Article
• 署名作者: Van der Laan, G.; Talman, D. A. J. J.; Yang, Z.
• 署名单位: Vrije Universiteit Amsterdam; Tinbergen Institute; Vrije Universiteit Amsterdam; Tilburg University; Tilburg University; Yokohama National University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0696-y
• 发表日期: 2006
• 页码: 127-134
• 关键词: extra dimension; fixed-points; algorithms

摘要

In this paper we present two theorems on the existence of a discrete zero point of a function from the n-dimensional integer lattice Z(n) to the n-dimensional Euclidean space R-n. The theorems differ in their boundary conditions. For both theorems we give a proof using a combinatorial lemma and present a constructive proof based on a simplicial algorithm that finds a discrete zero point within a finite number of steps.