Related papers: Hermite interpolation with retractions on manifold…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
The interpolation on Grassmann manifolds in the framework of parametric evolution partial differential equations is presented. Interpolation points on the Grassmann manifold are the subspaces spanned by the POD bases of the available…
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional…
We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, $J$-Hermitian, Hamiltonian and…
We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise naturally in scientific computing applications involving simulations, adjoint-enabled components,…
Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by…
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific…
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible curves subject to some interpolation conditions. The given…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary…
We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold reconstruction where a smooth $n$-dimensional submanifold…
In this paper, we investigate the interpolation of surfaces which are obtained from an isoasymptotic curve in 3D-Euclidean space. We prove that there exist a unique $ C^0 $-Hermite surface interpolation related to an isoasymptotic curve…
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…
Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…
The article completes the research of two-point G$^2$ Hermite interpolation problem with spirals by inversion of conics. A simple algorithm is proposed to construct a family of 4th degree rational spirals, matching given G$^2$ Hermite data.…