15、斯蒂费尔流形和格拉斯曼流形上的样条插值

斯蒂费尔流形和格拉斯曼流形上的样条插值

1. 斯蒂费尔流形上的C1解算法

在斯蒂费尔流形 $M$ 上进行插值时，有一个专门的算法来求解C1解。以下是该算法的详细步骤：

Algorithm 8 C1 Solution on the Stiefel manifold M. 
Input: N ≥ 3, (X0, ..., X N ) a matrix of size  N (n + 1) × N containing the (N + 1) interpolation 
points on M. 
Output: cY 
1: for i = 1 : N − 1 do 
2:
    Compute Z = [Zi 
    0, ..., Zi 
    N]T a matrix of size  N (n + 1) × N containing the (N + 1) 
    interpolation points on TXi M. 
3:
    for k = 0 : N do 
4:
        Zi 
        k = LogXi (Xk ) 
5:
        Compute Bi = [(Bi 
        1)−, ..., (Bi 
        N −1)−]T a matrix of size  N (n − 1) × N containing the 
        (N − 1) control points of the C1 Bézier curve βi on TXi M, using Algorithm 3. 
6:
        Compute control poin