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A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…

Optimization and Control · Mathematics 2021-09-28 Masoud Ahookhosh , Yurii Nesterov

In the 90's a collection of Plethystic operators were introduced in [3], [7] and [8] to solve some Representation Theoretical problems arising from the Theory of Macdonald polynomials. This collection was enriched in the research that led…

Combinatorics · Mathematics 2014-05-05 Francois Bergeron , Adriano Garsia , Emily Leven , Guoce Xin

We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…

Numerical Analysis · Mathematics 2016-05-24 Evan Gawlik , Melvin Leok

The $\alpha$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis…

Classical Analysis and ODEs · Mathematics 2025-09-22 Jamshid Saeidian , Bahareh Nouri

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…

Classical Analysis and ODEs · Mathematics 2018-01-17 Peter Kuchment , Sergey Lvin

Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…

Machine Learning · Computer Science 2023-03-15 Shizhe Ding , Boyang Xia , Milong Ren , Dongbo Bu

We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…

Functional Analysis · Mathematics 2018-09-05 Sergey V. Astashkin , Konstantin V. Lykov , Mario Milman

The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…

Numerical Analysis · Mathematics 2022-09-21 Francesco Dell'Accio , Federico Nudo

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

Classical Analysis and ODEs · Mathematics 2020-05-11 Asha Ram Gairola , Karunesh Kumar Singh

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…

Complex Variables · Mathematics 2022-09-27 José Oscar González-Cervantes , Juan Bory-Reyes

In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…

Mathematical Physics · Physics 2016-05-25 Michael Keyl , Jukka Kiukas , Reinhard F. Werner

Motivated by existing blend-to-zero techniques, a formal framework is developed for defining and constructing blend-to-zero operators on closed intervals for the generation of sufficiently smooth transitions between functions. Such…

Classical Analysis and ODEs · Mathematics 2026-04-30 Ivan Méndez-Cruz , Faisal Amlani

A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…

Numerical Analysis · Mathematics 2007-05-23 Ana Marco , Jose-Javier Martinez

In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…

Numerical Analysis · Mathematics 2025-05-21 Martin Buhmann , Joaquín Jódar , Miguel L. Rodríguez

Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general…

Functional Analysis · Mathematics 2018-04-24 Joseph A. Ball , Vladimir Bolotnikov , Sanne ter Horst

In a recent paper (2024) Camacho, C\'{a}novas, Mart\'{\i}nez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility…

Functional Analysis · Mathematics 2025-01-14 Nicolas Hadjisavvas

As a generalization of Hermite interpolation problem, Birkhoff interpolation is an important subject in numerical approximation. This paper generalizes the existing Generalized Recursive Polynomial Interpolation Algorithm (GRPIA) that is…

Numerical Analysis · Mathematics 2026-01-29 Xue Jiang , Yuanhe Li , Zhe Li

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…

Numerical Analysis · Mathematics 2013-09-11 E. Fuselier , T. Hangelbroek , F. J. Narcowich , J. D. Ward , G. B. Wright

Classical Gon\v{c}arov polynomials are polynomials which interpolate derivatives. Delta Gon\v{c}arov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental…

Combinatorics · Mathematics 2016-10-07 Rudolph Lorentz , Salvatore Tringali , Catherine H. Yan

After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see Labbas, Maingot and Thorel [14], leads us to consider, to study and to invert the sum of linear…

Analysis of PDEs · Mathematics 2024-03-06 Rabah Labbas , Stéphane Maingot , Alexandre Thorel