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Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…

Signal Processing · Electrical Eng. & Systems 2020-01-28 Niccolò Antonello , Lorenzo Stella , Panagiotis Patrinos , Toon van Waterschoot

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Pierre-François Marteau , Gilbas Ménier

We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…

Numerical Analysis · Mathematics 2023-05-23 Alessia andò , Dimitri Breda

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…

Machine Learning · Computer Science 2017-12-21 Dmitri S. Pavlichin , Jiantao Jiao , Tsachy Weissman

Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…

Rings and Algebras · Mathematics 2011-08-17 Vladimir P. Gerdt , Amir Hashemi , Benyamin M. -Alizadeh

We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.

Information Theory · Computer Science 2016-11-17 Graham H. Norton

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different…

Complex Variables · Mathematics 2018-12-10 Kamal Diki , Sorin G. Gal , Irene Sabadini

We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…

Numerical Analysis · Mathematics 2008-07-10 Joerg Kampen

The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…

Numerical Analysis · Mathematics 2024-12-06 Xiaobo Liu

A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…

Probability · Mathematics 2022-02-01 Lev Gelimson

Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…

Computer Vision and Pattern Recognition · Computer Science 2015-06-19 Emanuele Rodolà , Michael Moeller , Daniel Cremers

We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as…

Functional Analysis · Mathematics 2017-10-31 L Baratchart , Juliette Leblond , Fabien Seyfert

Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a…

High Energy Physics - Lattice · Physics 2009-11-07 Andrei Alexandru , Anna Hasenfratz

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…

Numerical Analysis · Mathematics 2017-12-27 Yoshihito Kazashi

An extensive table of pairs of functions linked by the Legendre transformation is presented. Many special functions and formulas that are used in the sciences are included in the pairs. Formulations are provided for finding the Legendre…

Classical Analysis and ODEs · Mathematics 2022-08-11 Quinn T. Kolt , Steven J. Kilner , David L. Farnsworth

Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…

Optimization and Control · Mathematics 2019-09-10 Carlos Ugaz , Lanshan Han , Alvin Lim

The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…

Numerical Analysis · Computer Science 2018-12-03 Pierre Ablin , Jean-François Cardoso , Alexandre Gramfort

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…

Optimization and Control · Mathematics 2011-12-08 Jesus A. De Loera , Peter N. Malkin , Pablo A. Parrilo

We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…

Numerical Analysis · Mathematics 2018-08-07 Aleš Vavpetič , Emil Žagar

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.

Functional Analysis · Mathematics 2011-04-25 Wen-Ming Lu , Lin Zhang