相关论文: Enhanced and Generalized One-Step Neville Algorith…
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.
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
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 a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small…
In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex…
We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of…
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has…
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a…
We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to form a small eigenproblem which is solved exactly. The two…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
This document describes an algorithm to scale a complex vector by the reciprocal of a complex value. The algorithm computes the reciprocal of the complex value and then scales the vector by the reciprocal. Some scaling may be necessary due…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in 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…