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...
Radial basis functions: basics, advanced topics and meshfree methods for transport problems.
Rational interpolation: analytical solution.
Rationale Interpolation, Normalität und Monosplines.
Reduced Piecewise Bivariate Hermite Interpolations.
Reference points based recursive approximation
The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...
Reference points based transformation and approximation
Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new -point transformation that yields a function with a simpler geometrical structure than the original function. It uses reference points and decreases the polynomial degree by . Then a general representation of polynomials is proposed based on reference...
Relèvement polynômial de traces et applications
Reliable Rational Interpolation.
Ritz-Galerkin Approximations in Blending Function Spaces.
Sard Kernel Theorems on Triangular Domains with Application to Finite Element Error Bounds.
Several notes on the circumradius condition
Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how the case...
Shape preserving rational cubic interpolation.
Simultaneous L1 Approximation of a Compact Set of Real-Valued Functions.
Smooth approximation of data with applications to interpolating and smoothing
In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.
Smooth approximation spaces based on a periodic system
A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system ....
Smooth local interpolation of surfaces using normal vectors.
Smoothing and interpolation in a convex subset of a Hilbert space : II. The semi-norm case
Solving Theodorsen's Integral Equation for Conformai Maps with the Fast Fourier Transform and Various Nonlinear Iterative Methods.