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.
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2$\begingroup$ Note: Dekker's method does not actually choose the better of bisection or the secant method. One could say Dekker's method is extremely reliant on using the secant method and will only use bisection instead when it really has to. $\endgroup$ Commented Sep 14, 2020 at 22:19