两线性流形之间夹角的算法(英文)

An Algorithm for Calculating the Angle Between Two Linear Manifolds

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.