The best algebraic approximation in Hölder norm.
The best approximation of the sinc function by a polynomial of degree with the square norm.
The best uniform quadratic approximation of circular arcs with high accuracy
In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples...
The evaluation of the remainders in approximation formulas by linear positive operators of interpolatory type.
The hp-version of the boundary element method with quasi-uniform meshes in three dimensions
We prove an a priori error estimate for the hp-version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The underlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surfaces, and for sufficiently smooth given data, the solution is H1-regular whereas, on open surfaces, edge...
The least solution for the polynomial interpolation problem.
The Lebesgue constant for Lagrange interpolation on equidistant nodes.
The Lower Estimate for Bernstein Operator
MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.
The powers of the bivariate Bernstein operators.
The response of skin friction, wall heat transfer and pressure drop to wall waviness in the presence of buoyancy.
The second order modulus again: some still (?) open problems.
The sharpness of convergence results for -Bernstein polynomials in the case
Due to the fact that in the case the -Bernstein polynomials are no longer positive linear operators on the study of their convergence properties turns out to be essentially more difficult than that for In this paper, new saturation theorems related to the convergence of -Bernstein polynomials in the case are proved.
The Weierstrass theorem on polynomial approximation
In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.
The weighted BMO condition and a constructive description of classes of analytic functions satisfying this condition.
Theoretical consideration of charge simulation method for numerical conformal mappings in a ring domain.
Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method.
Tres teoremas de aproximación en el espacio Lp mediante polinomios de coeficientes enteros.
Trigonometric Polynomial Approximation in the L1-Form.