Die Eindeutigkeit L2-optimaler Polynomialer Monosplines.
Die Güte der Lp-Approximation durch Kantorovic-Polynome.
Dini-Campanato spaces and applications to nonlinear elliptic equations.
Discrete, Linear Approximation Problems in Polyhedral Norms.
Discrete linear interpolatory operators.
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...
Effectiveness of transposed inverse sets in Faber regions.
Eigenvalues in the large sieve inequality, II
We explore numerically the eigenvalues of the hermitian formwhen . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Ein Funktionstheoretischer Beweis des Satzes von Müntz.
Eine Verschärfung der Abschätzung des Restes Taylorscher Näherungspolynome.
Éléments finis et l'estimation de l'erreur intérieur de la convergence
Equivalence Between K-functionals Based on Continuous Linear Transforms
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 bounds for eigenvalues and eigenfunctions of some ordinary differential operators by the method of least squares
Error estimates for modified local Shepard’s formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard’s partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard’s formulas, and...
Error estimates for Modified Local Shepard's Formulas in Sobolev spaces
Interest in meshfree methods in solving boundary-value problems has grown rapidly in recent years. A meshless method that has attracted considerable interest in the community of computational mechanics is built around the idea of modified local Shepard's partition of unity. For these kinds of applications it is fundamental to analyze the order of the approximation in the context of Sobolev spaces. In this paper, we study two different techniques for building modified local Shepard's formulas, and...
Estimates for En (Xn + 2m).
Estimations de l'erreur d'approximation par splines d'interpolation et d'ajustement d'ordre (m, s).
Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier.
Exact bounds for some basis functions of approximation operators.
Experiment on numerical conformal mapping of unbounded multiply connected domain in fundamental solutions method.