Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method

• Published in: Applied mathematics and computation Vol. 451; no. C; p. 127981
• Main Authors: Aristizabal, Mauricio, Hernández-Estrada, José L., Garcia, Manuel, Millwater, Harry
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 15.08.2023; Elsevier
• Subjects: Catenary; Elastic cable; Hypercomplex numbers; Newton-Raphson; Nonlinear equations; Elastic cable; Catenary; Nonlinear equations; Hypercomplex numbers; Newton-Raphson

•The traditional Newton-Raphson method to solve systems of nonlinear equations is enhanced to compute the required Jacobian with machine precision by applying hypercomplex perturbations to the degrees of freedom of the problem.•Arbitrary-order derivatives of the solution to the system of equations w...