What question did this study set out to answer?

The goal is to develop and evaluate an improved Newton-type method for solving nonlinear equations with higher convergence rates.

July 11, 2026Soft ComputingOpen Access

A third-order-convergence improved Newton method and its numerical performance

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Randomized trial demonstrates improved iterations in solving nonlinear equations, indicating enhanced efficiency.

The goal is to develop and evaluate an improved Newton-type method for solving nonlinear equations with higher convergence rates.
Utilized a rational approximation model with linear numerator and denominator for the iterative scheme.
Conducted numerical experiments to compare performance with traditional Newton's method and another third-order method.
Analyzed the basin of attraction for convergence characteristics.
The improved Newton method reduced the number of iterations compared to the traditional Newton's method.
Computational efficiency of the new method was comparable to that of another existing third-order method.
The method demonstrated superior characteristics in the convergence region and boundary complexity.

Saheya et al. (2026) studied this question.

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