Halley Method

The third order Halley's method for root finding of a Non-Linear equation.

the code is a function that inputs the initial guess for the method and outputs two arguments, first one is the converged root to the specified accuracy, and the second one is the iteration count to converge to that perticular threshold.

Important to note

1. the code contains the function as 'f', the first derivative of the function as 'f1' and the second derivate as 'f2'. to go with a different function, you have to update all these.
2. the error threshold is chosen as 1e-10. can be updated anytime.
3. the function is designed to get input in both scalars and arrays of scalars (when the input is given as an array, the output will be an array of the same size with points diverged or converged). the count, on the other hand, is not programmed to give reasonable output for an array input (it would be a healthy exercise to program it by yourself).