A Class of Multidimensional Periodic Splines.
A conjecture on multivariate polynomial interpolation.
La generalización de las fórmulas de interpolación de Lagrange y Newton a varias variables es uno de los temas habituales de estudio en interpolación polinómica. Dos clases de configuraciones geométricas particularmente interesantes en el plano fueron obtenidas por Chung y Yao en 1978 para la fórmula de Lagrange y por Gasca y Maeztu en 1982 para la de Newton. Estos últimos autores conjeturaron que toda configuración de la primera clase es de la segunda, y probaron que el recíproco no es cierto....
A Convergence Condition for the Quadrilateral Wilson Element.
A fast algorithm for scalar Nevanlinna-Pick interpolation.
A General framework for local interpolation.
A heuristic algorithm for constructing optimal lookup tables in circuit design.
A Method for Computing the Tension Parameters in Convexity-Preserving Spline-in-Tension Interpolation.
A moment problem for discrete nonpositive measures on a finite interval.
A New Algorithm for Osculatory Rational Interpolation.
A new kind of numeical tables of functions made by mathematical spectra
A Note on Polynomial Splines with Free Knots.
A note on the rate of convergence for Chebyshev-Lobatto and Radau systems
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
A Numerical study of Newton interpolation with extremely high degrees
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL...
A particular smooth interpolation that generates splines
There are two grounds the spline theory stems from - the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called smooth interpolation introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline...
A priori error estimates for Lagrange interpolation on triangles
We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation....
A property of divided differences with multiple nodes.
A Simple Rational Spline and its Application to Monotonic Interpolation to Monotonic Data.
A Table of Good Lattice Points in Three Dimensions.
A Useful Identity for the Rational Hermite Interpolation Table.
A variational approach to spline functions theory.