Computing all the roots of ∑iaiλ−ci=1 equations by a matrix-based approach

A useful procedure for finding all the roots of the type of equation indicated in the title, typically used in vapor–liquid separations, is presented. The proposed procedure is the result of a matrix-based analysis to generate a Standard Eigenvalue Problem. The eigenvalues of the resulting matrix system are exactly the roots of the equation indicated in the title. Numerical experiments are presented to show the goodness of the proposed procedure.

▸ We studied equations typically used in short-cut and flash distillation calculations. ▸ The proposed procedure is the result of a matrix-based analysis. ▸ All the roots are found using Standard Eigenvalue Problem solution technique. ▸ We do not need to make any prevision if some roots are near an equation's pole. ▸ All the roots of equations are found without the need of initial guesses.