Related papers: A trivariate interpolation algorithm using a cube-…
This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
We introduce a computational method for global optimization of structure and ordering in atomic systems. The method relies on interpolation between chemical elements, which is incorporated in a machine learning structural fingerprint. The…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
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…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Next generation radio-interferometers, like the Square Kilometre Array, will acquire tremendous amounts of data with the goal of improving the size and sensitivity of the reconstructed images by orders of magnitude. The efficient processing…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.
We propose a light-weight video frame interpolation algorithm. Our key innovation is an instance-level supervision that allows information to be learned from the high-resolution version of similar objects. Our experiment shows that the…
HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…
This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient…
We are concerned with the fastest possible direct numerical solution algorithm for a thin-banded or tridiagonal linear system of dimension $N$ on a distributed computing network of $N$ nodes that is connected in a binary communication tree.…
This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error…
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 presents an efficient parallel Adaptive Inverse Distance Weighting (AIDW) interpolation algorithm on modern Graphics Processing Unit (GPU). The presented algorithm is an improvement of our previous GPU-accelerated AIDW algorithm…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…
The adaptive partition of unity interpolation method, introduced by Aiton and Driscoll, using Chebyshev local interpolants, is explored for interpolating functions with sharp gradients representing two-medium problems. For functions that…