Keywords

Rationale

For historical reasons, an algorithm is proposed in Section A9.6.6 and A11.6.6 to solve a non-linear equation. The standard requires achieving an accuracy of 2 %. This level of accuracy can also be obtained by finding the intersection graphically, although nowadays probably no laboratory would use that approach. In the next section, it is shown that the ASTM proposed algorithm is not the most efficient and that very marginal effort is needed to increase the accuracy from 2 % to 0.01 % or machine precision (10-15). Currently, many non-linear solver tools exist that are embedded in various software packages. Using any of these tools, the mathematical effort to converge to an accuracy much better than 2 % is ridiculously low (less than 11 function evaluations, or iterations, to achieve machine precision). In order to ensure that the result of the analysis of standard data sets is not affected by the mathematical resolution of the linear equation, it is proposed to reduce the allowable error to less than 0.1 %. It is also proposed to leave the selection of the algorithm to the user, as such algorithms are currently embedded in many software packages and include many safeguards against numerical instabilities.