Related papers: Generalised Interpolation by Solving Recursion-Fre…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of…
We present a boundary integral method for solving a certain class of Riemann-Hilbert problems known as the general conjugation problem. The method is based on a uniquely solvable boundary integral equation with the generalized Neumann…
Mixup - a neural network regularization technique based on linear interpolation of labeled sample pairs - has stood out by its capacity to improve model's robustness and generalizability through a surprisingly simple formalism. However, its…
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…
Video frame interpolation, the task of synthesizing new frames in between two or more given ones, is becoming an increasingly popular research target. However, the current evaluation of frame interpolation techniques is not ideal. Due to…
This paper proposes a novel variant of hyperinterpolation, called hard thresholding hyperinterpolation. This approximation scheme of degree $n$ leverages a hard thresholding operator to filter all hyperinterpolation coefficients, which…
Room Impulse Responses estimation is a fundamental problem in spatial audio processing and speech enhancement. In this paper, we build upon our previously introduced diffusion-based inpainting framework for Room Impulse Response…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…
Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
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…
We investigate the enumeration of varieties of boolean theories related to Horn clauses. We describe a number of combinatorial equivalences among different characterizations and calculate the number of different theories in $n$ variables…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
This paper addresses the problem of interpolating visual textures. We formulate this problem by requiring (1) by-example controllability and (2) realistic and smooth interpolation among an arbitrary number of texture samples. To solve it we…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
Constrained Horn Clauses (CHCs) have conventionally been used as a low-level representation in formal verification. Most existing solvers use a diverse set of specialized techniques, including direct state space traversal or…