nth root algorithm
This online calculator implements nth root algorithm to find the principal nth root of a positive real number.
This page exists due to the efforts of the following people:
 | Timur
|
This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8311/. Also, please do not modify any references to the original work (if any) contained in this content.
Out of curiosity, this calculator implements nth root algorithm. This is iterative algorithm which is said to be very fast-converging, so the calculator lists the results of each iteration: current computed root value and current delta from previously computed root value. Calculator stops the iterations when desired precision is obtained, in other words, when the delta between previous and current computed roots is less than a precision. The description of the algorithm can be found below the calculator.
nth root algorithm
nth root algorithm
The algorithm is quite simple.
Step 1. Make an initial guess
In this calculator to get initial guess I simply divide number by root's degree if number is more than 1, and multiply by root's degree otherwise.
Step 2. Set
.
For precision check, it is more practical to compute delta separately
.
Step 3. Repeat step 2 until the desired precision is reached:
.
The algorithm can be derived from Newton's method for
,
where x is the root, and A is positive real number.
Comments