The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations considering fixed point and an initial guess value on the x-axis. The concepts of slope of a line and Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with computational efficiency index 1.414 and informational efficiency 1. The validity of the algorithm is examined by solving some examples and their comparisons with the Newton’s method.
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Gorashiya et al. (2024) studied this question.
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