A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds

DOI10.1016/j.cam.2016.07.018zbMath1357.53044OpenAlexW2478828246MaRDI QIDQ730522

Krzysztof A. Krakowski, Jorge Batista, Fátima Silva Leite, Luís Machado

Publication date: 28 December 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.07.018

zbMATH Keywords

Grassmann manifoldscanonical metricinterpolation problemsStiefel manifoldsquasi-geodesicsCasteljau algorithm

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Geodesics in global differential geometry (53C22) Ordinary differential equations and systems on manifolds (34C40) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35)

Related Items (7)

Extremal curves on Stiefel and Grassmann manifolds ⋮ A Numerical Algorithm for $C^2$-Splines on Symmetric Spaces ⋮ A multi-parameter family of metrics on Stiefel manifolds and applications ⋮ First order optimality conditions and steepest descent algorithm on orthogonal Stiefel manifolds ⋮ The cubic de Casteljau construction and Riemannian cubics ⋮ A Lagrangian approach to extremal curves on Stiefel manifolds ⋮ Efficient quasi-geodesics on the Stiefel manifold

Uses Software

• mftoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric mean and geodesic regression on Grassmannians
• Geodesics in infinite dimensional Stiefel and Grassmann manifolds
• Exposed faces and duality for symmetric and unitarily invariant norms
• Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
• The De Casteljau algorithm on Lie groups and spheres
• De Casteljau's algorithm on manifolds
• Bézier curves and \(C^{2}\) interpolation in Riemannian manifolds
• A two-step algorithm of smooth spline generation on Riemannian manifolds
• A New Geometric Algorithm to Generate Smooth Interpolating Curves on Riemannian Manifolds
• The Geometry of Algorithms with Orthogonality Constraints
• Functions of Matrices

This page was built for publication: A modified Casteljau algorithm to solve interpolation problems on Stiefel manifolds