Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry

作     者：felipe cucker Felipe CUCKER

作者机构：Department of MathematicsCity University of Hong KongHong KongChina 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2018年第39卷第2期

页      面：373-396页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by a GRF grant from the Research Grants Council of the Hong Kong SAR(No.CityU 11310716) 

主　　题：代数学 几何学 计算 复杂性分析 格子 数字算法 数字地 集合 

摘      要：In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.