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Equivalence Between K-functionals Based on Continuous Linear Transforms

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University....

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

Estimates for spline projections

J. H. Bramble, A. H. Schatz (1976)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Exponential expressivity of ReLU k neural networks on Gevrey classes with point singularities

Joost A. A. Opschoor, Christoph Schwab (2024)

Applications of Mathematics

We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains D ⊂ ℝ d , d = 2 , 3 . We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in D , comprising the countably-normed spaces of I. M. Babuška and B. Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high...

Fractional Korovkin Theory Based on Statistical Convergence

Anastassiou, George A., Duman, Oktay (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.

Fractional Trigonometric Korovkin Theory in Statistical Sense

Anastassiou, George A., Duman, Oktay (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 41A25, 41A36.In the present paper, we improve the classical trigonometric Korovkin theory by using the concept of statistical convergence from the summability theory and also by considering the fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.

How to increase convergence order of the Newton method to 2 × m ?

Sanjay Kumar Khattri (2014)

Applications of Mathematics

We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high...

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

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