I am beginner ,but I am keen interest to know which convergence method will always give root to the equation is it Newton or false method I am confused
2026-03-29 17:43:56.1774806236
Numerical convergence of root
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Bracketed methods like the bisection method or regula falsi have the guarantee that they converge towards a solution, the cost is that you need to start with an interval with a sign change of the function. Finding such an interval is not guaranteed to be easy.
Other methods like Newton or the secant method converge faster, if they converge at all. You have no sign conditions on the initial point, so you can easily try out different initial points.