TY - JOUR
T1 - Bézier Splines Interpolation on Stiefel and Grassmann Manifolds
AU - Adouani , Ines
AU - Samir , Chafik
JO - Journal of Computational Mathematics
VL - 6
SP - 1554
EP - 1578
PY - 2024
DA - 2024/11
SN - 42
DO - http://doi.org/10.4208/jcm.2303-m2022-0201
UR - https://global-sci.org/intro/article_detail/jcm/23507.html
KW - Optimization, Bézier spline, Curve fitting, Grassmann manifolds, Stiefel manifolds, Canonical metrics.
AB - <p style="text-align: justify;">We propose a new method for smoothly interpolating a given set of data points on
Grassmann and Stiefel manifolds using a generalization of the De Casteljau algorithm. To
that end, we reduce interpolation problem to the classical Euclidean setting, allowing us
to directly leverage the extensive toolbox of spline interpolation. The interpolated curve
enjoy a number of nice properties: The solution exists and is optimal in many common
situations. For applications, the structures with respect to chosen Riemannian metrics are
detailed resulting in additional computational advantages.</p>