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Related papers: Natural superconvergence points for splines

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In this work, we study superconvergence properties for some high-order orthogonal polynomial interpolations.The results are two-folds: When interpolating function values, we identify those points where the first and second derivatives of…

Numerical Analysis · Mathematics 2012-04-27 Zhimin Zhang

We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept [6] that transforms optimal quadrature rules from…

Numerical Analysis · Mathematics 2015-11-13 Michael Barton , Victor Calo

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

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

Optimization and Control · Mathematics 2020-02-26 Julian Rasch , Antonin Chambolle

Belmans, Oberdieck, and Rennemo asked whether natural automorphisms of Hilbert schemes of points on surfaces can be characterized by the fact that they preserve the exceptional divisor of non-reduced subschemes. Sasaki recently published…

Algebraic Geometry · Mathematics 2024-07-03 Patrick Girardet

This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {\it 2k-conjecture}: at each vertex of the underlying rectangular mesh, the…

Numerical Analysis · Mathematics 2014-01-03 Waixiang Cao , Zhimin Zhang , Qingsong Zou

In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth…

Optimization and Control · Mathematics 2023-07-31 Jiang Hu , Tonghua Tian , Shaohua Pan , Zaiwen Wen

The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the…

Numerical Analysis · Mathematics 2021-09-02 Ruming Zhang

This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…

Optimization and Control · Mathematics 2019-09-10 Xinlei Yi , Shengjun Zhang , Tao Yang , Karl H. Johansson , Tianyou Chai

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution…

General Relativity and Quantum Cosmology · Physics 2015-05-18 Isabel Cordero-Carrión , José María Ibáñez , Juan Antonio Morales-Lladosa

We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…

Image and Video Processing · Electrical Eng. & Systems 2022-06-28 Icíar Lloréns Jover , Thomas Debarre , Shayan Aziznejad , Michael Unser

We present a polynomial partitioning theorem for finite sets of points in the real locus of an irreducible complex algebraic variety of codimension at most two. This result generalizes the polynomial partitioning theorem on the Euclidean…

Algebraic Geometry · Mathematics 2015-09-22 Saugata Basu , Martin Sombra

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…

Numerical Analysis · Computer Science 2011-07-22 Annapurna Sharma , Hakimjon Zaynidinov , Hoon Jae Lee

We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…

Information Theory · Computer Science 2015-04-24 Yuanxin Li , Yuejie Chi

The paper proposes, an algorithm to produce novel m-point (for any integer m>=2) binary non-stationary subdivision scheme. It has been developed using uniform trigonometric B-spline basis functions and smoothness is being analyzed using the…

Numerical Analysis · Mathematics 2013-02-06 Shahid S. Siddiqi , Muhammad Younis

In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…

Disordered Systems and Neural Networks · Physics 2019-08-14 Ariel G. Meyra , Guillermo J. Zarragoicoechea , Alberto. L. Maltz , Enrique Lomba , Salvatore Torquato

We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…

Numerical Analysis · Mathematics 2019-04-01 Constantin Bacuta , Jacob Jacavage

The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…

Numerical Analysis · Mathematics 2016-01-19 Long Chen

This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson…

Numerical Analysis · Mathematics 2018-04-17 J. Pfefferer , M. Winkler

The Euler characteristic of a very affine variety encodes the number of critical points of the likelihood equation on this variety. In this paper, we study the Euler characteristic of the complement of a hypersurface arrangement with…

Algebraic Geometry · Mathematics 2024-12-31 Bernhard Reinke , Kexin Wang