Grid Search Algorithm

New to Julia
1

Hello,

I’m really new to programming and want to create a programm that uses the newton method to find the zero points of a function. To do that I need the differentiated function. I’m supposed to differentiate numerically by using f(x)-f(x-1)/x-(x-1). I have no idea how im supposed to implement this into Julia. Any help would be much appreciated. Thanks in advance.

2

Hi!, welcome to the julia community!
there is packages that can do that for you, for example:
you can directly derivate using ForwardDiff (better than numerical aproximation and faster than symbolic derivation)
if you are looking for the univariate newton algorithm, there is Roots.jl, it has a lot of algorithms, including the newton one.
if you need to implement this yourself as a part of a course, we can help you too, do you have something in mind?

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3

the grid search if i remember correctly implies finding zeros of a multivariate function in one direction iteratively, here is a newton implementation in julia, that is one part of the grid search algorithm:

function mynewton(f,df,x0,tol=1e-08,itermax=100) #here i give optional
# arguments, so later i don't need to write it in the function
    xiplus1 = zero(eltype(x0)) #basically 0.0, but more adaptable
    #good to remember that 1 and 1.0 are of distinct type, the first one is
    #an integer, the second one is a float
    xi = x0
    #main loop
    tolf=1000
    iter_count=0
    while (tolf>=tol) && (iter_count<=itermax) #the loop stops
        # if the tolerance or the maximum number of iterations is achieved
        xiplus1 = xi - f(xi)/df(xi)
        tolf = abs(f(xiplus1))
        iter_count+=1 #it adds 1 to the variable
        xi = xiplus1
    end
    return xiplus1
end
4

have a look at my package

https://github.com/chakravala/Fatou.jl

it uses my package Reduce.jl for symbolic differentiation

unless you have some really weird function, I’d recommend a symbolic over finite difference

5

Is this a homework problem?

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