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Root Route (Posted on 2004-06-29) Difficulty: 3 of 5
Develop an efficient algorithm to find the square root of a positive real number.

No Solution Yet Submitted by Gamer    
Rating: 2.2000 (5 votes)

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Solution Three iterations | Comment 2 of 7 |
To approximate the square root of N, set X to N and then iterate replacing X by (X^2+N)/(2X).

2nd method: replace X by (X^3+3NX)/(3X^2+N).

3rd method: replace X by (X^4+6NX^2-N^2)/(8X^3).

The first one is the classic Newton method; I worked out the next two by myself though these results may also be old and well known --just not by me!



  Posted by Oskar on 2004-06-29 08:25:56
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