A General Three-Step Class of Optimal Iterations for Nonlinear Equations

Table 3

Test function, their roots, and the starting points.

Test functions	Roots	Guess
𝑓1=sin(tan(𝑥)+𝑥)−12	0.2588298273352688443917065956960	0.4
𝑓2=sin(𝑥)−𝑥+2	2.55419595283704303782966617379187	2
𝑓3=𝑥^5−2𝑥+2cos(𝑥)	−1.25644837202179610636347166071080	−1.3
𝑓4=2cos(𝑥)+sin(𝑥)−𝑥	1.37318816571803393434603174397956	1.5
𝑓5=2𝑥^3−𝑥cos(𝑥)+1𝑥^2	−0.94316510784112785413792698729205	−0.8
𝑓6=𝑥^9+𝑥^4−𝑥^3+𝑥^2+14	−1.41582823891434741754690479611753	−1.4
𝑓7=𝑥^9−14sin(𝑥)	−1.33663345183152516454641803558884	−1.31
𝑓8=sin(𝑥^2+𝑥−3)+𝑥	0.931908190324955905662501231761206	1.5
𝑓9=cos(𝑥^2+𝑥−3)+𝑥^3	0.671280744928817559650708950129257	1
𝑓10=𝑥tan𝑥+𝑥	−0.785398163397448309615660845819875	−0.6
𝑓11=𝑥^4+13𝑥−1+tan𝑥	0.714180223545189655580041854721814	1
𝑓12=𝑥^30−𝑥−1+sin𝑥	1.004983564135382106859677582107315	1