In the first part of the paper we discuss minimal smoothness assumptions for the components of the solution decomposition which allow to prove robust convergence results in the energy norm for linear or bilinear finite elements on Shishkin meshes applied to convectiondiffusion problems with exponential boundary layers. In the corresponding derivation the standard Lagrange interpolant is used, i...

This paper addresses the problem of interpolating three points with a surface whose normal and orientation is also defined at those points. Conditions are derived for the existence of a quadric surface interpolant and it is shown that a cubic interpolant always exists. Finally, the paper describes a new cubic construction that provides a family of suitable surfaces with four geometrically intui...

This is a study of Favard interpolation—in which the nth derivatives of the interpolant are bounded above by a constant times the nth divided differences of the data—in the case the data is given on some subset of a rectangular lattice in R k. In some instances, depending on the geometry of this subset, we construct a Favard interpolant, and in other instances, we prove that none exists.

Cumulative chord C piecewise-cubics, for unparameterized data from regular curves in R , are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C piecewise-cubic interpolant. Theoretical estimates of orders of approximation are establis...

A Craig interpolant for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. An interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. We will discuss a number of applications of this concept in finiteand infinite-state model check...

A traditional interpolation model is characterized by the choice of reg-ularizer applied to the interpolant, and the choice of noise model. Typically , the regularizer has a single regularization constant , and the noise model has a single parameter. The ratio == alone is responsible for determining globally all these attributes of the interpolant: its`complexity', ``exibility', `smoothness', `...

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid.The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are bas...

In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using derivatives are presented. The combination tension, continuity, bias control is used as a very powerful type interpolation; they applied to curves. Surface construction utilizing studied explored several examples obtained by C1 surface given show usefulness method.

A powerful and versatile method of shape-preserving interpolation is developed in terms of piecewise exponential functions with a tension factor associated with each interval. Knots coincide with data points, and the interpolant is formulated in terms of its values and first derivatives at these points. For a given set of derivatives, this enables the efficient computation of the minimum tensio...