A SIMPLICIAL ALGORITHM FOR COMPUTING AN INTEGER ZERO POINT OF A MAPPING WITH THE DIRECTION PRESERVING PROPERTY

• 来源期刊: 计算数学（英文版）
• 关键词: Integer Zero Point Direction Preserving Simplicial Algorithm Triangulation Existence.
• 年，卷（期）: 2006,（6）
• 页码范围: 711-718
• 页数: 8页
• 语种: 英文

摘要

A mapping f: Zn → Rn is said to possess the direction preserving property if fi (x) ＞ 0 implies fi(y) ≥ 0 for any integer points x and y with ‖ix - y‖∞≤ 1. In this paper,a simplicial algorithm is developed for computing an integer zero point of a mapping with the direction preserving property. We assume that there is an integer point x0 with c ≤ x0 ≤ d satisfying that max1≤i≤n(xi - xi0)fi(x) ＞ 0 for any integer point x with f(x) ≠ 0 on the boundary of H = {x ∈ Rn | c- e ≤ x ≤ d + e}, where c and d are two finite integer points with c ≤ d and e = (1, 1, ... , 1)T ∈ Rn. This assumption is implied by one of two conditions for the existence of an integer zero point of a mapping with the preserving property in van der Laan et al. (2004). Under this assumption, starting at x0,the algorithm follows a finite simplicial path and terminates at an integer zero point of the mapping. This result has applications in general economic equilibrium models with indivisible commodities.