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We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…

Number Theory · Mathematics 2025-02-25 Guido Lido

By applying hybrid functions of general block-pulse functions and the second Chebyshev polynomials,integrodifferential systems are converted into a system of algebraic equations. The approximate solutions of integrodifferential systems are…

Numerical Analysis · Mathematics 2008-04-30 Xing Tao Wang

It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…

Optimization and Control · Mathematics 2018-04-30 Le Dung Muu , Phung Minh Duc , Xuan Thanh Le

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…

Information Theory · Computer Science 2015-07-14 Steffen Limmer , Jafar Mohammadi , Slawomir Stanczak

In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…

Quantum Physics · Physics 2019-07-08 Yassine Hamoudi , Frédéric Magniez

We show how polynomial mappings of degree k from a union of disjoint intervals onto [-1,1] generate a countable number of special cases of a certain generalization of the Chebyshev Polynomials. We also derive a new expression for these…

Classical Analysis and ODEs · Mathematics 2007-05-23 Y. Chen , J. C. Griffin , M. E. H. Ismail

We derive closed-form expressions for the poles and zeros of approximate fractional integrator/differentiator filters, which correspond to spectral roll-off filters having any desired log-log slope to a controllable degree of accuracy over…

Computational Engineering, Finance, and Science · Computer Science 2016-06-21 Julius Orion Smith , Harrison Freeman Smith

We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients…

Algebraic Geometry · Mathematics 2022-11-15 Alperen A. Ergür , Timo de Wolff

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…

Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor…

Computational Physics · Physics 2015-12-01 Pankaj K Mishra , Sankar K Nath

This paper considers the approximation of a monomial $x^n$ over the interval $[-1,1]$ by a lower-degree polynomial. This polynomial approximation can be easily computed analytically and is obtained by truncating the analytical Chebyshev…

Numerical Analysis · Mathematics 2021-01-19 Arvind K. Saibaba

We derive a stronger uniqueness result if a function with compact support and its truncated Hilbert transform are known on the same interval by using the Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert transform,…

Machine Learning · Computer Science 2020-02-13 Jason You

In this paper, we propose distributed algorithms that solve a system of Boolean equations over a network, where each node in the network possesses only one Boolean equation from the system. The Boolean equation assigned at any particular…

Optimization and Control · Mathematics 2021-03-04 Hongsheng Qi , Bo Li , Rui-Juan Jing , Lei Wang , Alexandre Proutiere , Guodong Shi

In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…

Optimization and Control · Mathematics 2024-10-01 Tan Nhat Pham , Minh N. Dao , Andrew Eberhard , Nargiz Sultanova

Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…

Cosmology and Nongalactic Astrophysics · Physics 2023-08-09 Nicholas Choustikov , Zvonimir Vlah , Anthony Challinor

We investigate a fully discrete finite element approximation for the stochastic Kuramoto-Sivashinsky equation, combining the standard finite element methods in spatial discretization with the implicit Euler-Maruyama scheme in time. Rigorous…

Numerical Analysis · Mathematics 2025-10-08 Hung D. Nguyen , Liet Vo

This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one…

Optimization and Control · Mathematics 2026-01-13 Jose de Brito , Felipe Lara , Tran Van Thang

It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate functions from few samples. So far, theoretical guarantees are…

Numerical Analysis · Mathematics 2023-07-24 Felix Bartel , Kai Lüttgen , Nicolas Nagel , Tino Ullrich

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao