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What is the fastest way to compute cube root?

0 votes

Detail algo with code may be helpful?

posted Nov 16, 2015 by Brijesh Talwar

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2 Answers

+1 vote

Suppose we want to find cube root of a, that is, we wish to solve x^3 - a = 0. Apply Newton Raphson method, that is, apply iterative method
xn+1 = xn - f(xn)/ f'(xn), where f(x) = x^3 - a, f'(x) = 3x^2, so the process is
xn+1 = xn - (xn/3 - a/(3xn^2) = ( 2xn + a/xn^2)/ 3

answer Nov 17, 2015 by Ramesh Chand Mittal
0 votes

Perfect Solution Ramesh, Just iterating more with example -

Cube root of a number a is obtained by starting with a guess x1 of the cube root and using the formula
x2 = (1/3)[2 x1 + a/(x1^2)]

So say to find the cube root of 5, we take x1 as 3/2. (This guess is based on the reasoning that a value of 2 will be too high since the cube of 2 is 8 wheres as a value of 1 is too low since the cube of 1 is 1)

So x2 = (1/3)(2(3/2) + 5/(9/4)) = 1 + 20/27 = 47/27. We then let x1 = 47/27 and repeat the process, successively finding better and better approximations to the cube root of 5.

answer Nov 17, 2015 by Salil Agrawal
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