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A novel predictive homotopic path tracking algorithm to solve non-linear algebraic equations |
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| Authors: | María de la Luz López-González Miriam Lucero Quemada-Villagómez Gloria María Martinez-González Juan Manuel Oliveros-Muñoz Hugo Jiménez-Islas |
| Affiliation: | 1. Tecnologico Nacional de México en Celaya, Departamento de Ingeniería Bioquímica, Guanajuato, Mexico
Contribution: Conceptualization, Formal analysis, Methodology, Software, Validation, Writing - review & editing;2. Tecnologico Nacional de México en Celaya, Departamento de Ingeniería Bioquímica, Guanajuato, Mexico Contribution: ?Investigation, Resources, Software, Validation, Visualization;3. Tecnologico Nacional de México en Celaya, Departamento de Ingeniería Química, Guanajuato, Mexico Contribution: Data curation, ?Investigation, Methodology, Supervision, Writing - original draft;4. Universidad Iberoamericana Torreón, Departamento de Ingenierías, Arquitectura y Diseño, Torreón, Mexico Contribution: Conceptualization, ?Investigation, Methodology, Writing - original draft;5. Tecnologico Nacional de México en Celaya, Departamento de Ingeniería Bioquímica, Guanajuato, Mexico |
| Abstract: | In chemical engineering and other areas of mathematics and engineering sciences, systems of non-linear algebraic equations often must be solved, and a problem is that these types of systems often cannot be solved analytically. Homotopic continuation methods are globally convergent and can find several solutions to the analyzed algebraic system and consist of a predictive step followed by a corrective step, which can cause reversion of homotopic path tracking. Therefore, in this work, the use of a homotopy continuation method (HCM) based on a purely predictive methodology is proposed; that is, it only makes use of predictor vectors (without correction vectors) to find the solution to several systems of non-linear algebraic equations with a multiplicity of solutions, employing lower central proccessing unit (CPU) time in comparison with standard homotopic tracking algorithms. |
| Keywords: | homotopic continuation non-linear algebraic equations only predictive homotopic path tracking |