Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration.
We study -splines (existence, uniqueness and convergence) in Banach spaces with a view to applications in approximation. Our approach allows, in particular, considering some problems in a more regular domain, and hence facilitating their solution.
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...