REVIEW 1 cited by
Fractional Newton-Raphson Method Accelerated with Aitken's Method
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the derivative is different from one. A simplified way of constructing the Riemann-Liouville (R-L) fractional operators, fractional integral and fractional derivative, is presented along with examples of its application on different functions. Furthermore, an introduction to the Aitken's method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, to finally present the results that were obtained when implementing the Aitken's method in the F N-R method.
Forward citations
Cited by 1 Pith paper
-
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.
Discussion (0). Continue with ORCID to comment.