Comparison of Derivative-free Method and Finite-difference Method for Singular Systems (original) (raw)

2021, Acta Polytechnica Hungarica

In this paper, the derivative-free method for solving singular systems is compared with the classical finite-difference method for nonlinear systems. Since the convergence rate of an iterative method to singular solution drops down, the convergence can be accelerated by forming the bordered system. Left and right singular vectors of the finitedifference approximation of the Jacobian are used for the construction of the bordered system. The local algorithm for finding a solution is tested on several examples and compared with the finite-difference method. The obtained numerical results, which are promising, indicate fast local convergence of the proposed derivative-free method and point out that it has better performances than the finite-difference method.

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