To secure a numerically stable computation of the matrix G, the Gegenbauer polynomials are evaluated with the aid of their recurrence relation (12).
For each of the N (N+1)/2 matrix entries which have to be computed we
need 3 arithmetic operations for the scalar products of the
vectors 
and 
and 
arithmetic operations for the
evaluation of the Gegenbauer-polynomials using the recurrence
relation (12). Thus, the computation of G
requires 
arithmetic operations.
Because of the symmetry of G we used Cholesky-decomposition to solve the
system of equations (13).
This requires 
operations.
The calculation of the weights therefore needs 
arithmetic operations.