Variance-Optimal Data Approximation Using the Abel-Jacobi Functions

Conditions are found under which d-dimensional linear interpolating spaces \(\mathcal{L}_d \) generated by the classical Abel-Jacobi elliptic functions contain constants and are variance optimal with respect to the equidistant d-design χ d . The so-called modulus parameter k = k(d) of the Abel-Jacobi functions is assumed to belong to (−1, 1) ∪ i R. The spaces \(\mathcal{L}_d \) are optimal if k(d) is restricted to i R when d is odd, with no such restriction needed when d is even.