Derivative-Free Quasi-Newton–Type Scheme for Singular Nonlinear Equations With Fuzzy Coefficients

Newton’s algorithm is among the effective solution schemes for nonlinear systems of equations. This scheme is guaranteed to converge for a nonsingular Jacobian of the system in the solution neighborhood, and the convergence rate is quadratic. However, any violation of the stated condition, for instance, the Jacobian being singular, would result in unsatisfactory convergence, which may even be lost. In response, this study presents a derivative-free quasi-Newton scheme for singular nonlinear equations with fuzzy coefficients. The method uses a safeguarded diagonal Jacobian approximation, avoiding singularity issues and reducing computational cost. Linear convergence is proved under standard assumptions. Preliminary findings on a set of benchmark problems highlight the efficacy of the developed scheme.