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You are not logged in. #1 20090627 07:57:13
Calculating square rootsI came across this interesting method the other day, but I have no idea how it works. It does seem reliable though. Why did the vector cross the road? It wanted to be normal. #2 20090627 10:01:34
Re: Calculating square rootsFiguring out why a method works is interesting, just remember that nothing works as fast as Newton's method. (Actually I'm using Newton's method right now to calculate the initial conditions for a pde that models heat/gas mixture in an engine) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20090627 11:06:38
Re: Calculating square rootsHi, Last edited by bobbym (20090627 11:37:28) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20090629 11:06:31
Re: Calculating square roots. . . . . . . . . . . . . . . . . . . . . . . . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . . . #5 20090629 20:48:08
Re: Calculating square rootsThis is a specific case of Newton's method, which takes an approximation a and puts it through Why did the vector cross the road? It wanted to be normal. #6 20090629 23:23:55
Re: Calculating square roots
mathsyperson could you furnish the reference where you found this method. The intermediate values are iterated with this (2x(base)+e)e if you are in base 10 (the decimal system) then with x representing all of the previous digits (estimates) The series of e's are the sucessive digits of the square root of the number, until you reach the desired tolerance wanted. For each iteration e will produce a digit of the square root of n. If in base 10 the first digit or initial x is #7 20090630 03:20:44
Re: Calculating square rootsI was just shown that method by a friend who thought it was cool. Why did the vector cross the road? It wanted to be normal. #8 20090630 03:43:39
Re: Calculating square rootsHi Integer; Last edited by bobbym (20090630 04:44:16) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20090630 06:23:30
Re: Calculating square rootsThanks, mathsyperson #10 20090630 06:35:57
Re: Calculating square rootsHi integer; Now drop the e^2 because it is much smaller than the e. You are left with Solve for e This has quadratic convergence and as mathsyperson explains above is a variant of newtons. Actually your whole method starting with is the error analysis way to derive newtons iteration. Last edited by bobbym (20090630 06:50:45) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 