leja
Leja points, or Leja sequences, refer to a method for choosing interpolation nodes in a compact subset of the complex plane. They are used in polynomial interpolation, numerical quadrature, and related approximation tasks. The construction is greedy: select the first point x1 in the target set; for n ≥ 2, choose xn in the set to maximize the product ∏_{k=1}^{n-1} |xn − xk|. In practice, this means each new point tends to be as far as possible, in a multiplicative sense, from the previously chosen points. The resulting sequence provides a stable foundation for interpolating polynomials of increasing degree and often yields favorable conditioning of the associated Vandermonde matrices.
Leja sequences have variants on specific domains, such as the unit disk or the unit circle, and
Applications include constructing interpolation grids for spectral methods, developing quadrature rules, and analyzing polynomial approximation behavior