As an optional assignment in a Numerical Analysis class I have the task of creating a hybrid root finding algorithm that uses both the Secant and Bisection method. I have only started learning about numerical methods so I am unsure of what is the deciding factor that makes me switch from Bisection to Secant and vice versa while the program is running? What is the condition(s) I should be looking for?
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You could try something similar to Dekker's method by doing both secant and bisection and then choosing the better one for the next iteration.