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Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the $W^{1, p}$ -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the $p = \infty$ case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how the case...

Shape preserving rational cubic interpolation.

Muhammad Sarfraz (1993)

Extracta Mathematicae

Shape-from-Shading, viscosity solutions and edges.

P.L. Lions, E. Rouy, A. Tourin (1993)

Numerische Mathematik

Sharp bounds on the mathematical constant e.

Khattri, Sanjay Kumar (2009)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Sharp error bounds for some quadrature formulae and applications.

Ujević, Nenad (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Sharp error estimates for the numerical differentiation formulas on the classes of entire functions of exponential type.

Vinogradov, O.L. (2007)

Sibirskij Matematicheskij Zhurnal

Sharp Estimates in Terms of Moduli of Smoothness for Compound Cubature Rules.

R.J. Nessel, B. Büttgenbach, ... (1989/1990)

Numerische Mathematik

Simple Monte Carlo integration with respect to Bernoulli convolutions

David M. Gómez, Pablo Dartnell (2012)

Applications of Mathematics

We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit...

Simulation of an approximate optimal decomposition in breakpoints in approximating the function $f (x) = x^{n}$ by a broken line

Karel Beneš (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Simulation of analog computer in solving non-linear differential equations by a digital computer

Karel Beneš (1984)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Simultaneous L1 Approximation of a Compact Set of Real-Valued Functions.

M.P. Carroll (1972)

Numerische Mathematik

Singular Splines.

Paula P. Chan (1972/1973)

Numerische Mathematik

Smooth approximation of data with applications to interpolating and smoothing

Segeth, Karel (2013)

Programs and Algorithms of Numerical Mathematics

In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.

Smooth approximation spaces based on a periodic system

Segeth, Karel (2015)

Programs and Algorithms of Numerical Mathematics

A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $exp (- k x)$ ....

Smooth contour line construction with spline interpolation.

Pere Brunet Crosa, Lluis Pérez Vidal (1984)

Qüestiió

Contour maps are frequently used to represent three-dimensional surfaces from geographical applications or experimental results. In this paper, two new algorithms for the generation and display of such contours are presented. The first of them uses local spline interpolation to obtain contour maps from data points in a rectangular mesh, whereas the other interpolates a set of irregular points through recursive subdivision of triangles. In both algorithms, precision of the contours can be adjusted...

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