Introduction: Impact craters on the Moon (and other bodies) form and degrade over time resulting in a change in crater shape and hence an overall evolution in lunar topography. Modeling of crater erosion (e.g. [1, 2, 3]) enables the tracking of crater shape evolution with time and can be used to estimate the relative age of a particular crater. Intuitively, crater degradation results from the c...

We construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss-Chebyshev-Lobatto quadrature. The underlying function is sampled at N ∼ n/2 points, whereas the hyperinterpolation polynomial is determined by its (n + 1)(n + 2)(n...

In paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...

We derive simple Chebyshev polynomial approximations for the density function and cumulative distribution function of the Chernoff distribution. They provide 6 significant figure accuracy with extreme efficiency.

A common practice for computing an elementary transcendental function nowadays has two phases: reductions of input arguments to fall into a tiny interval and polynomial approximations for the function within the interval. Typically the interval is made tiny enough so that one won’t have to go for polynomials of very high degrees for accurate approximations. Often approximating polynomials as su...

We show that Lagrange interpolants at the Chebyshev zeros yield best relative polynomial approximations of ð1þ ðaxÞÞ 1 on 1⁄2 1; 1 ; and more generally of Z N

ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...