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Finding Square Root Using the Newton Rhapson Method

Demonstrates the method for finding square root using the Newton Rhapson method, which is commonly used in calculators

Submitted By: erik.price

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Views: 196

Language: Java

Last Modified: November 6, 2009

Instructions: Similar to the bisection method in design, but this method will perform better in almost every case (excluding perfect numbers, it'll find the answer, but just in a few more iterations)

Snippet

public static double newtonSqrt(double x, double epsilon)
{
int ctr = 0; //ctr makes sure that the function will terminate eventually
double guess = 10; //initial guess to check
double result = guess-((guess*guess-x)/(2*guess));
if(x < 0){
return Double.longBitsToDouble(0x7ff8000000000000L);
//this represents NaN (Not-a-Number) because negative
//square roots don't work so well
}
else if(x == 0){
return 0; //prevents it from returning an incorrect answer
}
while((Math.abs(result*result - x) > epsilon) && ctr < 1000)
{
guess = result;
result = guess - ((guess*guess-x)/(2*guess));
ctr++;
}
return result;
//note: you can remove the epsilon variable from the method and replace it with an unchanging hardcoded value for set precision
}