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Volume 42, Issue 6
Bézier Splines Interpolation on Stiefel and Grassmann Manifolds

Ines Adouani & Chafik Samir

DOI: 10.4208/jcm.2303-m2022-0201

J. Comp. Math., 42 (2024), pp. 1554-1578.

Published online: 2024-11

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  • Abstract

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.

  • Keywords

Optimization, Bézier spline, Curve fitting, Grassmann manifolds, Stiefel manifolds, Canonical metrics.

  • AMS Subject Headings

49K15, 65D10, 49K30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1554, author = {Adouani , Ines and Samir , Chafik}, title = {Bézier Splines Interpolation on Stiefel and Grassmann Manifolds}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {1554--1578}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2303-m2022-0201}, url = {http://global-sci.org/intro/article_detail/jcm/23507.html} }
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 -

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.

Adouani , Ines and Samir , Chafik. (2024). Bézier Splines Interpolation on Stiefel and Grassmann Manifolds. Journal of Computational Mathematics. 42 (6). 1554-1578. doi:10.4208/jcm.2303-m2022-0201
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