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udvat 101 Nov 30, 2008 at 11:50

For a function, I want to calculate the range where one root exists. For example, f(x) has a root in subrange [a1,b1], another root in subrange[a2,b2] in a total range of [X,Y]. Is any such algorithm available to calculate the ranges?

Thanks in advance.

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Reedbeta 167 Nov 30, 2008 at 19:04

Can you give us any more details about the function? For a completely general function, this sort of thing is not really possible. However if you have a specific class of functions you are interested in (such as polynomials) then it may be possible.

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Sol_HSA 119 Dec 01, 2008 at 06:53

Or how about not posting schoolwork assignments?

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udvat 101 Dec 01, 2008 at 06:55

Thanks for your reply.
My desired function is 10sin(x)-x=0.

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Reedbeta 167 Dec 01, 2008 at 09:28

Well I’ll give you a hint.

You know (or should know) that sin(x) is always between -1 and 1. Given this, you should be able to calculate a range of x values where that function could possibly have roots.

Once you’ve done that, you can use what you know about where the roots of sin(x) are to estimate how many roots your function could have and ranges where they could be.

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udvat 101 Dec 01, 2008 at 09:28

I found the method “Bracketing method” in the following link

http://civilwares.free.fr/27102005/Applied%20Numerical%20Methods%20with%20MATLAB%20for%20Engineers%20and%20Scientists/cha92657_ch05.pdf

It works fine for my purpose. Thanks to all.