Two results on polynomial interpolation in equally spaced points

Two Results on Polynomial Interpolation in Equally Spaced Points

We present two results that quantify the poor behavior of polynomial interpolation in n equally spaced points. First, in band-limited interpolation of complex exponential functions e‘li (c( E Iw), the error decreases to 0 as n + a, if and only if d( is small enough to provide at least six points per wavelength. Second, the Lebesgue constant ,4. (supremum norm of the nth interpolation operator) ...

Adaptive Polynomial Interpolation on Evenly Spaced Meshes

The problem of oscillatory polynomial interpolants arising from equally spaced mesh points is considered. It is shown that by making use of adaptive approaches that the oscillations may be contained and that the resulting polynomials are data bounded and monotone on each interval. This is achieved at the cost of using a different polynomial on each sub-interval. Computational results for a numb...

Approximate Fekete Points for Weighted Polynomial Interpolation

We compute approximate Fekete points for weighted polynomial interpolation by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function. Moreover, we apply the method to the construction of real and complex weigh...

Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials

We prove a conjecture of Ambrus, Ball and Erdélyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form n X

On polynomial interpolation of two variables