A Computational Procedure for the Approximation of Random Functions.
A conjecture related to the approximation operators of binomial type.
A counterexample in comonotone approximation in space
Refining the idea used in [24] and employing very careful computation, the present paper shows that for 0 < p ≤ ∞ and k ≥ 1, there exists a function , with for x ∈ [0,1] and for x ∈ [-1,0], such that lim supn→∞ (en(k)(f)p) / (ωk+2+[1/p](f,n-1)p) = + ∞ where is the best approximation of degree n to f in by polynomials which are comonotone with f, that is, polynomials P so that for all x ∈ [-1,1]. This theorem, which is a particular case of a more general one, gives a complete solution...
A Discrepancy Theorem Concerning Polynomials of Best Approximation in L...[-1, 1].
A general theorem on triangular finite -elements
A generalization of Hermite interpolation.
A Korovkin type approximation theorems via -convergence
Using the concept of -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.
A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients.
A lower bound for the second moment of Schoenberg operator.
A method for summability of Lagrange interpolation.
A new exceptional polynomial for the integer transfinite diameter of
Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials.
A new generating function of (-) Bernstein-type polynomials and their interpolation function.
A new H(div)-conforming p-interpolation operator in two dimensions
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable...
A new H(div)-conforming p-interpolation operator in two dimensions
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) -1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. We show that this operator is stable with...
A Note on a Result of Zolotarev and Bernstein.
A note on Diophantine approximation.
A note on lacunary approximation on [-1,1]
A note on polynomial approximation in Sobolev spaces
A note on polynomial approximation in Sobolev spaces
For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.
A note on simultaneous diophantine approximation.