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In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces…

Optimization and Control · Mathematics 2022-10-03 Henrik Eisenmann , Felix Krahmer , Max Pfeffer , André Uschmajew

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Numerical Analysis · Mathematics 2025-05-12 Abinash Nayak

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…

Numerical Analysis · Mathematics 2021-05-11 Jordi Feliu-Fabà , Lexing Ying

In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are…

Numerical Analysis · Mathematics 2012-11-16 Nikola Mirkov , Bosko Rasuo

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

Numerical Analysis · Mathematics 2026-01-27 Robin Herkert , Tobias Ehring , Bernard Haasdonk

A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them…

Commutative Algebra · Mathematics 2024-04-23 Anna Maria Bigatti , Elisa Palezzato , Michele Torielli

We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding to some initial geometry or material parameters, we can…

Numerical Analysis · Mathematics 2017-02-15 Victor Minden , Anil Damle , Kenneth L. Ho , Lexing Ying

In this paper we introduce the Higher Order Lipschitz Greedy Recombination Interpolation Method (HOLGRIM) for finding sparse approximations of Lip$(\gamma)$ functions, in the sense of Stein, given as a linear combination of a (large) number…

Numerical Analysis · Mathematics 2024-06-06 Terry Lyons , Andrew D. McLeod

The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…

Numerical Analysis · Mathematics 2020-08-04 Donatella Occorsio , Woula Themistoclakis

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…

Computer Vision and Pattern Recognition · Computer Science 2013-08-07 H. Lakshman , W. -Q Lim , H. Schwarz , D. Marpe , G. Kutyniok , T. Wiegand

The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…

Combinatorics · Mathematics 2023-10-05 Mohamed Amine Boutiche , Mohamed Mechacha , Mourad Rahmani

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…

Numerical Analysis · Mathematics 2023-10-05 Sven Beuchler , Tim Haubold , Veronika Pillwein

Consider $\{p_n\}_{n=0}^{\infty}$, a sequence of polynomials orthogonal with respect to $w(x)>0$ on $(a,b)$, and polynomials $\{g_{n,k}\}_{n=0}^{\infty},k \in \mathbb{N}_0$, orthogonal with respect to $c_k(x)w(x)>0$ on $(a,b)$, where…

Classical Analysis and ODEs · Mathematics 2021-10-27 A. S. Jooste , D. D. Tcheutia , W. Koepf

In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-09-30 Roman Gitlin

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

Numerical Analysis · Mathematics 2025-02-26 Mark Embree , Joel A. Henningsen , Jordan Jackson , Ronald B. Morgan

The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\lambda$). We propose an efficient way to interpolate the…

Machine Learning · Computer Science 2015-06-11 Da Kuang , Alex Gittens , Raffay Hamid

Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…

Numerical Analysis · Mathematics 2012-08-06 Michael Brandon Youngberg

We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that their difference probably has at most half the number of terms of…

Symbolic Computation · Computer Science 2014-01-24 Andrew Arnold , Mark Giesbrecht , Daniel S. Roche

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…

Dynamical Systems · Mathematics 2021-12-16 Mikołaj Myszkowski

This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…

Numerical Analysis · Mathematics 2026-01-08 Dhivya Prabhu K , Sanjeev Singh , Antony Vijesh