  Rational Krylov subspace projection methods are one of successful methods in
MOR, mainly because some order derivatives of the approximate and original
transfer functions are the same. This is the well known moments matching
result. However, the properties of points which are far from the interpolating
points are little known. In this paper, we obtain the error's explicit
expression which involves shifts and Ritz values. The advantage of our result
over than the known moments matches theory is, to some extent, similar to the
one of Lagrange type remainder formula over than Peano Type remainder formula
in Taylor theorem. Expect for the proof, we also provide three explanations for
the error formula. One explanation shows that in the Gauss-Christoffel
quadrature sense, the error is the Gauss quadrature remainder, when the Gauss
quadrature formula is applied onto the resolvent function. By using the error
formula, we propose some greedy algorithms for the interpolatory $H_{\infty}$
norm MOR.
