@misc{bah-rev-08-ab-compinc,
  author = {Baharev, Ali and R{\'e}v, Endre},
  title = {Comparing Inclusion Techniques on Chemical Engineering Problems},
  howpublished = {Online document submitted to the 13th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN); not in the proceedings?},
  year = 2008,
  month = sep,
  note = {A 2-page abstract.}
  url = {https://reliablecomputing.eu/baharev-scan08-abstract.pdf},
  abstract = {[\dots] Computing steady states of multistage separation processes requires solving large-scale nonlinear systems of equations. [\dots] computation of these problems with interval arithmetic have not yet been considered in the literature [\dots] The authors aim to compute steady states of homogeneous and heterogeneous azeotropic distillation columns with interval methods, keeping the algorithm as problem independent as possible. The results achieved so far
are presented here.  Numerical evidence published in the literature, e.g. [7, 8], seem to indicate superiority of the linear interval approximation (LIA, $L(x) = Ax+b$, $A$ is a real matrix), proposed by Kolev in a number of publications e.g. [9], compared to the traditional interval linear approximation (ILA, $L(x) = A(x − z) + f(z)$, $A$ is an interval matrix) such as the interval Newton method. LIA has the following advantages over ILA when applied to root-finding. (i) The solution set of the LIA has a much simpler form, the hull solution is straightforward: $X \cap − A^{−1} b$. (ii) Linear programming is directly applicable to prune the current box. The automatic computation of LIA is possible with affine arithmetic [10] which in turn (iii) automatically keeps track of correlation between the computed partial results yielding tighter enclosures. There is no significant difference in the computation time per iteration between LIA and ILA. In [11] LIA and ILA are compared as linearization techniques applying them to chemical engineering problems of real complexity. The examples considered are highly structured and are full of dependency. LIA outperforms the traditional ‘textbook’ interval Newton algorithm (IN/GS) by an order of magnitude in the case of the studied examples. Note that state-of-the-art variants of the interval Newton methods, e.g. [12, 13], also outperform the IN/GS used for comparison. Linear programming may be preferable as pruning technique for LIA because of its robustness. Considering the conclusions of [11], the \textbf{C++} class has been re-implemented, and the LP pruning method has been revised. The improvement is significant; real life medium-scale problems are successfully solved. Some of the problems used for comparison are suitable for benchmarks, they will
be contributed soon.}
}