In a recent paper, Y. Xu proposed a set of Chebyshev-like points for polynomial interpolation on the square [−1, 1]. We have recently proved that the Lebesgue constant of these points grows like log of the degree (as with the best known points for the square), and we have implemented an accurate version of their Lagrange interpolation formula at linear cost. Here we construct non-polynomial Xu-...

In recent years, comprehensive learning particle swarm optimization (CLPSO) has attracted the attention of many scholars for using in solving multimodal problems, as it is excellent in preserving the particles' diversity and thus preventing premature convergence. However, CLPSO exhibits low solution accuracy. Aiming to address this issue, we proposed a novel algorithm called LILPSO. First, this...

Let Pd(C ) denote the space of polynomials of degree at most d in n complex variables. A subset X of C – we will usually speak of configuration or array – is said to be unisolvent for Pd(C ) (or simply unisolvent of degree d) if, for every function f defined on X there exists a unique polynomial P ∈ Pd(C ) such that P(x) = f (x) for every x ∈ X. This polynomial is called the Lagrange interpolat...

This paper introduces a parallel algorithm for computing an N=n!-point Lagrange interpolation on an n-star (n>2). It exploits several communication techniques on stars in a novel way which can be adapted for computing similar functions. The algorithm is optimal and consists of three phases: initialization, main and final. While there is no computation in the initialization phase, the main phase...