CODEWITHSUNDEEP
gonewtons-method
Vishak Arudhra
Vishak Arudhra

Reputation: 63

Golang Newton Method Implementation - Major Confusion

CONTEXT

Among many intuitive solutions online, I've trying hard to understand this one implementation which was posted on r/golang.

Just to enrich the context, here's the problem statement in the golang tutorial:

As a way to play with functions and loops, let's implement a square root function: given a number x, we want to find the number z for which z² is most nearly x.

Here's the link to the post and here's the code from that post which I've slightly changed to understand it better:

package main

import (
    "fmt"
)

func Sqrt(x, z float64) float64 {

    z -= ((z*z - x) / (2*z))
    
    for z*z > x {
        z -= ((z*z - x) / (2*z))
    }
    return z
}

func main() {
    fmt.Println(Sqrt(100, 1))
}

DOUBT

How is it that for any given value of z and x, z^2 always ends up a greater value than x in the first iteration (that is before the beginning of the for loop)?

I have this doubt since I wonder if there's a way whereby both z^2 is less than x and the returned z is an incorrect root to x.

I'm mostly convinced that z^2 cannot be less than x in the first iteration since I couldn't find any combination of z and x proving otherwise, in so far as I could try. I would greatly appreciate an explanation as to why z^2 is always greater than x on the first iteration, if indeed that is true.

Upvotes: 1

Views: 123

Answers (1)

Mohammad Ansari
Mohammad Ansari

Reputation: 1549

this is because z -= ((z * z - x) / (2*z)) is equal to

z = z - ((z * z - x) / (2*z))

because in first place value of z is always way less than x so z * z - x will be negative

and we have z - (negative value ) so this will be positive for example a-(-b) = a+b

but as z starts to grow the value z*z - x will become less and less

Upvotes: 0

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