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This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…

Functional Analysis · Mathematics 2018-02-28 Zahid Akhtar , Muhammad Aqeel Ahmad Khan

We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space $X$ and an infinite-tensor-product Jacobi measure. For target infinite-variate functions taking…

Numerical Analysis · Mathematics 2026-02-02 Dinh Dũng , Van Kien Nguyen , Duong Thanh Pham , Christoph Schwab

In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…

Numerical Analysis · Mathematics 2025-03-04 Kazufumi Ito , Bangti Jin , Fengru Wang , Jun Zou

This paper is devoted to the computation of the asymptotic boundary terms in entropy methods applied to a fast diffusion equation with weights associated with Caffarelli-Kohn-Nirenberg interpolation inequalities. So far, only elliptic…

Analysis of PDEs · Mathematics 2016-11-15 Jean Dolbeault , Maria J. Esteban , Michael Loss

We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex…

Optimization and Control · Mathematics 2018-09-24 D. Russell Luke , Ron Shefi

In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of…

Numerical Analysis · Mathematics 2013-03-05 Victor Y. Pan

We study the Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion and with monotonically increasing initial data using the Riemann-Hilbert (RH) approach. The solution of the Cauchy problem, in the zero dispersion…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 T. Grava

In this paper we study those polynomials orthogonal with respect to a particular weight over the union of disjoint intervals first introduced by N.I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This…

Classical Analysis and ODEs · Mathematics 2007-05-23 Y. Chen , A. Its

We calculate the $k$-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for $k=1$ to derive a closed-form expression for eigenvalue density. For real matrices we…

Statistics Theory · Mathematics 2016-09-06 Tim Wirtz , Daniel Waltner , Mario Kieburg , Santosh Kumar

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…

Classical Analysis and ODEs · Mathematics 2020-07-22 Amparo Gil , Javier Segura , Nico M. Temme

We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grids methods constructed with the help of quasi-interpolation operators. The class of such operators includes classical…

Numerical Analysis · Mathematics 2021-11-12 Yurii Kolomoitsev , Tetiana Lomako , Segey Tikhonov

Solutions to differential equations, which are used to model physical systems, are computed numerically by solving a set of discretized equations. This set of discretized equations is reduced to a large linear system, whose solution is…

Numerical Analysis · Mathematics 2024-03-18 Mohit Tekriwal , Joshua Miller , Jean-Baptiste Jeannin

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

Optimization and Control · Mathematics 2025-11-19 Vitaliano S. Amaral , Marcio Antônio de A. Bortoloti , Jurandir O. Lopes , Gilson N. Silva

In this paper, we derive a Sampling Method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second-order…

Analysis of PDEs · Mathematics 2019-05-30 Isaac Harris

Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of…

Complex Variables · Mathematics 2017-04-11 Alexander I. Bobenko , Felix Günther

This paper discusses an abstract Kramer sampling theorem for functions within a reproducing kernel Hilbert space (RKHS) of vector valued holomorphic functions. Additionally, we extend the concept of quasi Lagrange-type interpolation for…

Functional Analysis · Mathematics 2024-08-26 Subhankar Mahapatra , Santanu Sarkar

This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…

Classical Analysis and ODEs · Mathematics 2022-08-10 S. B. Damelin , K. Diethelm

The goal of the paper is to obtain analogs of the sampling theorems and of the Riesz-Boas interpolation formulas which are relevant to the Discrete Hilbert and Kak-Hilbert transforms in $l^{2}$.

Classical Analysis and ODEs · Mathematics 2021-11-04 Isaac Pesenson

In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…

Numerical Analysis · Mathematics 2013-08-30 Zhiqiang Xu , Tao Zhou

The carr\'e du champ method is a powerful technique for proving interpolation inequalities with explicit constants in presence of a non-trivial metric on a manifold. The method applies to some classical Gagliardo-Nirenberg-Sobolev…

Analysis of PDEs · Mathematics 2022-02-16 Jean Dolbeault , An Zhang