Evaluation of a C-table

General algorithm of computation of c-table and detection of valleys

“…Thus, it is possible to expect that the application of the ascending algorithm gives more precise results. For the 9th column, this is, in fact, the case for rows [11][12][13][14]. Surprisingly, for the next columns, the descending algorithm gives better results, even solely with double precision and even if both numbers are very bad for rows 20 and 21.…”

“…If the element is nonzero, then relation (6) is applied and the element is computed. However, if the element is equal to zero, then the other formulas should be applied [the Gilewicz formula [2, p. 374] (formula (85)) or the Paszkowski formula [11]]. To decide which of these formulas is appropriate, the program checks the element located to the left for the ascending algorithm or above for the descending algorithm.…”

Computation of the -Table Related to the Padé Approximation

“…. (12). Then the cost of computed by (22) is = + + + + 4, where , , , and are the previous costs of , , , and , respectively.…”

“…No problems arise in a numerical computation if all coefficients are integers [8,12]. If a block exists, the integer arithmetic produces zeros exactly.…”

“…This formula given in [10,12] is given here in terms of Toeplitz and Hankel determinants. An extension of representations of using other determinants around the zeros block in thetable will be presented in the next section.…”