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The performed numerical analysis reveals that Wynn's identity for the compass$1/(N-C)+1/(S-C)=1/(W-C)+1/(E-C)=1/\eta$ (here C stands for center, the otherletters correspond to the four directions of the compass) gives the long soughtcriterion, the minimal $|\eta|$, for the choice of the optimal Pad\'eapproximant. The work of this method is illustrated by calculation ofmultipoint Pad\'e approximation by a new formula for calculation of this bestrational approximation. The work of the criterion for the calculation ofoptimal Pad\'e approximant is illustrated by the frequently seen in thetheoretical physics problems of calculation of series summation and multipointPad\'e approximation used as a predictor for solution of differential equationsmotivated by the magneto-hydrodynamic problem of heating of solar corona byAlv\'en waves. In such a way, an efficient and valuable control mechanism for$N$-point Pad\'e approximant calculation is proposed. We believe that thesuggested method and criterion can be useful for many applied problems innumerous areas not only in physics but in any scientific application wheredifferential equations are solved. The solution of the Cauchy-Jacobi problem isillustrated by a Fortran program. The algorithm is generalized for the case ofthe first $K$ derivatives at $N$ nodal points.

Robust formula for $N$-point Pad\'e approximant calculation based on Wynn identity