# Algorithm for Fractional power calculation

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Life is Wonderful on 28 Feb 2022
Edited: Life is Wonderful on 13 Mar 2022
Hi
1. fractional base is no problem with current implementation.
2. To support fractional exponents, get the n-th root for any given number b. How to implement algorithm to get a numerical approximation ?
3. Current approach is inefficient, because it loops e times
b = [-32:32]; % example input values
e = [-3:3]; % example input values but doesn't support fraction's
power_function(b,e)
p = 1;
if e < 0
e = abs(e);
multiplier = 1/b;
else
multiplier = b;
end
for k = 1:e
p(:) = p * multiplier; % n-th root for any given number
end

Alan Stevens on 28 Feb 2022
How about using the Newton-Raphson algorithm. Here's the basic idea:
% x^n = b
% Let f(x) = x^n - b
% dfdx(x) = n*x^(n-1)
%
% Use Newton-Raphson iteration
% x1 = initial guess
% err = 1;
% while err > tol
% x = x1 - f(x1)/dfdx(x1);
% err = abs(x - x1);
% x1 = x
% end
Walter Roberson on 12 Mar 2022
Sorry, I do not know.

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