Related papers: Hermite interpolation and data processing errors o…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis 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…
The adaptive cubic regularization algorithm employing the inexact gradient and Hessian is proposed on general Riemannian manifolds, together with the iteration complexity to get an approximate second-order optimality under certain…
In this note we present an alternative way to obtain optimal interpolation operators for two-grid methods applied to Hermitian positive definite linear systems. Falgout and Vassilevski in [SIAM J. Numer. Anal, 42 (2004), pp. 1669-1693] and…
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…
This paper presents a robust enhancement of the Tangent space Hermite Interpolation (THI) method for manifold-valued data by integrating the multivariate Arnoldi process. To circumvent the inherent numerical instability of multivariate…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
A new effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In…
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…
Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks…
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…
Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…