Spline prewavelets for non-uniform knots.
Spline quasi-interpolants and quadrature formulas.
Spline recurrences for quartic splines
Spline Representations of Functions in Besov-Triebel-Lizorkin Spaces on Rn.
Spline solutions for nonlinear two point boundary value problems.
Spline Subdivision Schemes for Compact Sets. A Survey
Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...
Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil II.
Splineapproximationen von beliebigen Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil III.
Splines and pseudo-inverses
Splines in Numerical Integration
AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...
Stability of quadratic interpolation polynomials in vertices of triangles without obtuse angles
An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: are the vertices of triangles without obtuse inner angles such that has one side common with for .
Stability results for scattered data interpolation on the rotation group.
Stability Theorems for Fourier Frames and Wavelet Riesz Bases.
Stable multiresolution analysis on triangles for surface compression.
Stable rank of Fourier algebras and an application to Korovkin theory.
Statistical approximation by positive linear operators
Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space into a weighted space .
Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers
In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.
Statistical approximation properties of q-Baskakov-Kantorovich operators
In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.
Statistical approximation to Bögel-type continuous and periodic functions
In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.
Statistical estimates for generalized splines
In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.