On the error estimation in numerical methods
On the Variational Characterization and Convergence of Bivariate Splines.
On Unordering Horvitz and Thompson's Tl -Class of Linear Estimators.
Optimal interpolatory splines using -spline representation
Optimal polygonal interpolation
Optimal problems concerning interpolation methods of solution of equations.
Optimal quadratic interpolatory splines on general knotset
Optimal-order quadratic interpolation in vertices of unstructured triangulations
We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...
Oscillation Matrices with Spline Smoothing.
Parametric and nonparametric empirical regression models: case study of copper bromide laser generation.
Polya conditions for multivariate Birkhoff interpolation: from general to rectangular sets of nodes.
Polynomial best constrained degree reduction in strain energy.
Polynomials and Vandermonde matrices over the field of quaternions.
Quadratic Interpolatory Splines.
Quadratic splines smoothing the first derivatives
The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights and smoothing parameter , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter is mentioned.
Quartic and biquartic interpolatory splines on simple grid
Quartic smoothing splines generalized
Quartic splines with minimal norms
Quartic X-Splines.
Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of ℝd, d ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming...