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Spline Interpolation on Other Riemannian Manifolds

In: Regression and Fitting on Manifold-valued Data

Author

Listed:
  • Ines Adouani

    (University of Sousse, Higher Institute of Applied Sciences and Technology of Sousse (ISSAT))

  • Chafik Samir

    (University of Clermont Auvergne (UCA))

Abstract

In this chapter, our objective is to extend and validate the methodology introduced in previous chapters to encompass additional cases of symmetric Riemannian manifolds. Specifically, we focus on two such instances: the set of symmetric and positive-definite matrices (SPD), denoted as $$\mathcal {P}_{n}^{+}$$ P n + , and hyperbolic spaces $$\mathcal {H}_{n}$$ H n characterized by constant negative curvature. These nonlinear spaces find wide-ranging applications where the demand for smooth interpolating splines is pronounced.

Suggested Citation

  • Ines Adouani & Chafik Samir, 2024. "Spline Interpolation on Other Riemannian Manifolds," Springer Books, in: Regression and Fitting on Manifold-valued Data, chapter 0, pages 149-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61712-6_9
    DOI: 10.1007/978-3-031-61712-6_9
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