Fractional Newton methods with a derivative order that changes during iteration find multiple real and complex roots of nonlinear systems from real initial guesses.
Fractional Newton-Raphson Method
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abstract
The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.
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math.NA 1years
2019 1verdicts
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Fractional Newton-Raphson Method and Some Variants for the Solution of Non-linear Systems
Fractional Newton methods with a derivative order that changes during iteration find multiple real and complex roots of nonlinear systems from real initial guesses.