两线性流形之间夹角的算法(英文)  

An Algorithm for Calculating the Angle Between Two Linear Manifolds

作　　者：张圣贵[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福州350007

出　　处：《工程数学学报》2013年第4期517-524,共8页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11071041)

摘　　要：本文将3维欧氏空间中直线与平面的夹角推广到n维欧氏空间中两线性流形的夹角,并用带线性和二次等式约束的二次规划刻画这个夹角,从而,把求两线性流形夹角的问题转化为求解非凸二次规划问题,由此,给出了计算这种夹角的一个算法和数值算例.在该数值算例中,我们应用Grbner基理论求解非凸二次规划问题.Generalizing the angle between a line space, we define the angle between and a plane in a 3-dimensional Euclidean two nontrivial linear manifolds in an ndimensional Euclidean space, which is characterized by a quadratic programming problem with constraints of linear and quadratic equations. Therefore, finding this angle is transformed to solving a non-convex quadratic programming problem. Thus, we present an algorithm for finding this angle, and give a numerical example. We solve the non-convex quadratic programming in this example by means of the GrSbner basis theory.

关 键 词：夹角 GROBNER基 非凸二次规划 

分 类 号：O221.2[理学—运筹学与控制论]