A rapidly convergent method for solving third-order polynomials
Source abstract
Abstract
We present a rapidly convergent method for solving cubic polynomial equations with real coefficients. The method is based on a power series expansion of a simplified form of Cardano’s formula using Newton’s generalized binomial theorem. Unlike Cardano’s formula and semi-analytical iterative root finders, the method is free from round-off error amplification when the polynomial coefficients differ by several orders of magnitude or when they do not differ much from each other, but are all large or small by many orders of magnitude. Validation of the method is assessed by casting a cubic equation of state as a polynomial in terms of the compressibility factor and the reduced molar volume for propylene at temperature and pressure conditions where Cardano’s formula and iterative root finders fail.
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Research context
OpenAlex topics: Iterative Methods for Nonlinear Equations · Phase Equilibria and Thermodynamics
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Affiliations
Universidad Politécnica Territorial de Mérida (UPTM), Grupo de Investigaciones de Ciencias Básicas y Aplicadas 1 , Av. 25 de Noviembre, Ejido 5251, Estado Mérida, Venezuela
Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana - Azcapotzalco (UAM-A) 2 , Av. San Pablo 180, 02200 Ciudad de México, Mexico
Centro de Física, Instituto Venezolano de Investigaciones Científicas (IVIC) 3 , Caracas 1020-A, Venezuela
Funding
This work has been supported by the Universidad Autónoma Metropolitana through internal funds.
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