Related papers: On iterated interpolation
Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads.…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…
Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that 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…
Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of…
In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The…