A Useful Identity for the Rational Hermite Interpolation Table.
A variational approach to spline functions theory.
Admissible Slopes for Monotone and Convex Interpolation.
Algebraically solvable problems: describing polynomials as equivalent to explicit solutions.
Algorithm 46. Determination of an interpolating quadratic spline function
Aliasing and Poisson Summation in the Sampling Theory of Paley-Wiener Spaces.
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An Algorithm for Computing Constrained Smoothing Spline Functions.
An Algorithmic Approach to Hermite-Birkhoff-Interpolation.
An approximation in the -norm by Hermite interpolation.
An Elementary Algebraic Representation of Polynomial Spline Interpolants for Equidistant Lattices and its Condition.
An error analysis for absolute and relative approximation.
An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
An example related to Whitney extension with almost minimal norm.
An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials
An Implementation of the Method of Ermakov and Zolotukhin for Multidimensional Integration and Interpolation.
An iterative Clough-Tocher interpolant
An operator-theoretic approach to theorems of the Pick-Nevanlinna and carathéodory types.
Analytic interpolation and the degree constraint
Analytic interpolation problems arise quite naturally in a variety of engineering applications. This is due to the fact that analyticity of a (transfer) function relates to the stability of a corresponding dynamical system, while positive realness and contractiveness relate to passivity. On the other hand, the degree of an interpolant relates to the dimension of the pertinent system, and this motivates our interest in constraining the degree of interpolants. The purpose of the present paper is to...
Anisotropic interpolation error estimates via orthogonal expansions
We prove anisotropic interpolation error estimates for quadrilateral and hexahedral elements with all possible shape function spaces, which cover the intermediate families, tensor product families and serendipity families. Moreover, we show that the anisotropic interpolation error estimates hold for derivatives of any order. This goal is accomplished by investigating an interpolation defined via orthogonal expansions.