Abstract
The Newdon Iterative method and its deformation mostly require calculating the derivative of nonlinear equations. In practice, many functions are complex, and there are limitations in finding high-order derivatives. This paper fits an existing iterative format by establishing n times interpolated polynomials, n conditions are used to construct a system of linear equations with n equations and n + 1 unknowns, in which the previous n unknowns can be expressed by the n + 1 th unknown by Clem’s rule, to achieve the purpose of reducing the number of derivative calculations. Convergence analysis and numerical examples verify that the algorithm is better than Newdon iteration, and can be better used in path trajectory optimization and fractional time delay control.
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