The Wynn identity as the long sought criterion for the choice of the optimal Padé approximant
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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) (here C stands for center, the other letters correspond to the four directions of the compass) gives the long sought criterion for the choice of the optimal Padé approximant. The work of this method is illustrated by calculation of multipoint Padé approximation a new formula for calculation of this best rational approximation. The work of criterion for the calculation of optimal Padé approximant is illustrated by the frequently seen in the theoretical physics problems of calculation of series summation and multipoint Padé approximation used as a predictor for solution of differential equations originated from the magneto-hydrodynamic problem of heating of solar corona by Alvén waves. In such a way, an efficient and valuable control mechanism for Padé approximant calculation is proposed. With this numerical enhancement, the ε-algorithm can be safely implemented in any commercial computation software and of course, can be independently used by any colleague in need of a robust numerical method for tackling a computational problem revealing the physical world.
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