  In a previous work, we show that the solution of the initial-boundary value
problem for the two-component nonlinear Schr\"odinger equation on the finite
interval can be expressed in terms of the solution of a $3\times 3$
Riemann-Hilbert problem. The relevant jump matrices are explicitly given in
terms of the three matrix-value spectral functions $s(k)$, $S(k)$ and $S_L(k)$,
which in turn are defined in terms of the initial values, boundary values at
$x=0$ and boundary values at $x=L$, respectively. However, for a well-posed
problem, only part of the boundary values can be prescribed, the remaining
boundary data cannot be independently specified, but are determined by the
so-called global relation. Here, we use a Gelfand-Levitan-Marchenko
representation to derive an expression for the generalized Dirichlet-to-Neumann
map to characterize the unknown boundary values in physical domain, which is
different from the approach, in fact it analyzed the global relation in
spectral domain, used in the previous work. And, we can show that these two
representations are equivalent.
