  In this work, we propose a new approach to the problem of critical point
calculation, based on the formulation of Heidemann and Khalil (1980). This
leads to a $2 \times 2$ system of nonlinear algebraic equations in temperature
and molar volume, which makes possible the prediction of critical points of the
mixture through an adaptation of the technique of inversion of functions from
the plane to the plane, proposed by Malta, Saldanha, and Tomei (1993). The
results are compared to those obtained by three methodologies: ($i$) the
classical method of Heidemann and Khalil (1980), which uses a double-loop
structure, also in terms of temperature and molar volume; ($ii$) the algorithm
of Dimitrakopoulos, Jia, and Li (2014), which employs a damped Newton algorithm
and ($iii$) the methodology proposed by Nichita and Gomez (2010), based on a
stochastic algorithm. The proposed methodology proves to be robust and accurate
in the prediction of critical points, as well as provides a global view of the
nonlinear problem.
