This paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λm,n. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λm,n(x) if m ≥ 2 is even.

Asymptotic and numerical analysis provides essential insight into the behaviour of Fourier integral solutions for the deflexion of an infinite continuously-supported flexible plate due to moving load. Thus we can define in detail how the plate deflexion depends upon the load speed, including (a) the wave patterns generated by a load moving steadily at various supercritical speeds; and (b) the time-dependent behaviour of the deflexion due to an impulsively-started load, where the two-dimensional response tends to a steady state except at the critical speed, when it grows continuously with time (in the absence of dissipation).

This is an expository paper in which we present an introduction to a variational approach to spline interpolation. We present a sequence of theorems which starts with Holladay's classical result concerning natural cubic splines and culminates in some general abstract results.

Some recent results on the optimal choice of quadrature rules for the finite element solution of eigenvalue problems are discussed in the light of some results of the author and J. Paine.

A boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.

An integro-differential equation of Prandtl's type and a collocation method as well as a collocation-quadrature method for its approximate solution is studied in weighted spaces of continuous functions.

CAD systems have traditionally catered for architectural and mechanical engineering designs which are somewhat constrained in scope. Problems concerning other types of design such as art design, industrial design or sculpting, where creativity and aesthetic factors play an important role, are not adequately addressed. These types of design require much more flexibility in both geometric modelling capability and user-machine interaction. This paper first gives a brief overview of recent work which deals with creative activities, and analyses important issues that need to be addressed in object representations for 3D creative activities. We then discuss a scheme to categorise and represent aesthetic factors in geometric modelling.

This is a short précis of a presentation on some of the recent advances in the area of extrapolation quadrature; given at David Elliott's 65th birthday conference in Hobart in February 1997.