Related papers: On iterated interpolation
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
Motivated by classical results of approximation theory, we define an Hermite-type interpolation in terms of $n$-dimensional subspaces of the space of $n$ times continuously differentiable functions. In the main result of this paper, we…
In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
Mixup refers to interpolation-based data augmentation, originally motivated as a way to go beyond empirical risk minimization (ERM). Yet, its extensions focus on the definition of interpolation and the space where it takes place, while the…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
A number of basic image processing tasks, such as any geometric transformation require interpolation at subpixel image values. In this work we utilize the multidimensional coordinate Hermite spline interpolation defined on non-equal spaced,…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
While direct statements for kernel based interpolation on regions $\Omega \subset \mathbb{R}^d$ are well researched, far less is known about corresponding inverse statements. The available inverse statements for kernel based interpolation…
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions…
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are…