Related papers: A priori error estimates for Lagrange interpolatio…

This paper introduces the novel concept of fractal interpolation over curves in Banach spaces. The contents are based on the usual methodologies involving the fractal interpolation problem over intervals but the current approach…

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…

We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are…

We derive a priori interior Hessian and gradient estimates for special Lagrangian equation of phase at least a critical value in dimension three.

Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art…

We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order…

Wavelet coefficients are estimated recursively at progressively coarser scales recursively. As a result, the estimation is prone to multiplicative propagation of truncation errors due to quantization and round-off at each stage. Yet, the…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…

In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates…

We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…

When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…

This work is an attempt to develop an approximate scheme for estimating the volume-based truncation errors in the finite volume analysis of laminar flows. The volume-based truncation error is the net flow error across the faces of a control…

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

We formulate the Lagrange-D'Alembert principle as a pure mathematical theory that meets modern standards of rigor. While we note several new aspects of the principle, the article is primarily methodological.

In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative…

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can…

In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.

A new alternative numerical procedure to the Szeg\H{o} quadrature formulas for the estimation of integrals with respect to a positive Borel measure $\mu$ supported on the unit circle is presented. As in many practical situations, we assume…