Summary: The interpolation problem of constructing a function holomorphic on the upper half-plane with values having nonnegative imaginary part and with continuous extension to the real axis by the first $2n+1$ terms of its asymptotic decomposition at infinity and its values at some $m$ points of the real axis is solved using algorithms which are reminiscent of those of Schur and Lagrange. Certain algorithms are obtained for construction of functions holomorphic on the upper half-plane with contractive values having continuous extension to the real axis by their values at some $m$ real points.