  Asymptotic approximations to the zeros of Jacobi polynomials are given, with
methods to obtain the coefficients in the expansions. These approximations can
be used as standalone methods for the non-iterative computation of the nodes of
Gauss--Jacobi quadratures of high degree ($n\ge 100$). We also provide
asymptotic approximations for functions related to the first order derivative
of Jacobi polynomials which are used for computing the weights of the
Gauss--Jacobi quadrature. The performance of the asymptotic approximations is
illustrated with numerical examples, and it is shown that nearly double
precision relative accuracy is obtained both for the nodes and the weights when
$n\ge 100$ and $-1< \alpha, \beta\le 5$. For smaller degrees the approximations
are also useful as they provide $10^{-12}$ relative accuracy for the nodes when
$n\ge 20$, and just one Newton step would be sufficient to guarantee double
precision accuracy in that cases.
