Question

How do you estimate real zeros

Answer 1

as in the newton method?

Answer 2

there is a numerical method that is just full of rote repetition...

start with a guess, plug it into the function; if the values is positive; subtract 1/2, if negative add 1/2 and reevaluate.

when the function changes sign on you from one step to the next; go back to the value in the last step and modify it by 1/4; and use 1/4 modifications until the sign changes again ans step back and modify by 1/8 ... then to 1/16 .... then to etc. all depending on how accurate you wanna make the estimate

Answer 3

the newton method is good for certain behaved functions; and its just another way to find the "next" x value to try out.

lets say g = your guess; then evaluate the function as follows

newGuess = f'(g)x -f'(g)g + f(g) = 0

now g = newGuess and repeat it ...

Answer 4

there are also error functions you can play in to it to get better and better approximataions. but thats the basics of it