How to do decimal search?

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Mesosleepy
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#1
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#1
How to do decimal search

Also, is there a quicker way to do it?
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Mesosleepy
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Andy98
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(Original post by Mesosleepy)
How to do decimal search

Also, is there a quicker way to do it?
Not heard of that method before, could you give me a rough idea of what it is?
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Mesosleepy
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(Original post by Andy98)
Not heard of that method before, could you give me a rough idea of what it is?
I'm not sure, but it is something to do with locating roots.
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Andy98
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(Original post by Mesosleepy)
I'm not sure, but it is something to do with locating roots.
Ohhhh, that thing. I can't remember the details, but you basically find an iterative formula and spam equals. Although TeeEm would be better at explaining it than me.
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TeeEm
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(Original post by Andy98)
Ohhhh, that thing. I can't remember the details, but you basically find an iterative formula and spam equals. Although TeeEm would be better at explaining it than me.
sorry but I am teaching at the moment
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Andy98
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(Original post by TeeEm)
sorry but I am teaching at the moment
Fair enough, sorry to disturb
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NotNotBatman
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#8
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Is it like the bisection method, but splitting the interval into ten instead of two? If it is, just substitute values of x into the equation of the curve and then the root lies in the interval where it goes from negative to positive or positive to negative.
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Gregorius
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#9
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(Original post by Mesosleepy)
How to do decimal search

Also, is there a quicker way to do it?
A decimal search is a particular variation of the change of sign method. First assume there is a unique root. If f(0) and f(1) are of different sign, then you know there is a root between 0 and 1. Divide the interval [0,1] into ten and check the end-points of each of these sub intervals. The sub-interval that has a change of sign on its end-points contains the root. Now subdivide that interval. Continue until you reach a preset accuracy threshold. Deal with the case of multiple roots in the obvious fashion.

There a many ways of finding roots; the Wikipedia article is a pretty reasonable introduction.
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Mesosleepy
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#10
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(Original post by Gregorius)
A decimal search is a particular variation of the change of sign method. First assume there is a unique root. If f(0) and f(1) are of different sign, then you know there is a root between 0 and 1. Divide the interval [0,1] into ten and check the end-points of each of these sub intervals. The sub-interval that has a change of sign on its end-points contains the root. Now subdivide that interval. Continue until you reach a preset accuracy threshold. Deal with the case of multiple roots in the obvious fashion.

There a many ways of finding roots; the Wikipedia article is a pretty reasonable introduction.
Can you give an example?
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Gregorius
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(Original post by Mesosleepy)
Can you give an example?
Let f(x) = x - pi

Then f(3) < 0 & f(4) > 0. So there is a root in [3,4].

Divide up [3,4] into ten equal sub-intervals.
Then f(3.0) < 0, f(3.1) < 0 - so not this interval,
f(3.1) < 0 & f(3.2) > 0 - this interval.

So divide up [3.1, 3.2] into ten sub-intervals. Then
f(3.10) < 0 & f(3.11) < 0 - not this interval
f(3.11) < 0 & f(3.12) < 0 - not this interval
f(3.12) < 0 & f(3.13) < 0 - not this interval
f(3.13) < 0 & f(3.14) < 0 - not this interval
f(3.14) < 0 & f(3.15) > 0 -this interval. So, divide up [3.14, 3.15] into ten etc etc...
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Mesosleepy
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#12
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(Original post by Gregorius)
Let f(x) = x - pi

Then f(3) < 0 & f(4) > 0. So there is a root in [3,4].

Divide up [3,4] into ten equal sub-intervals.
Then f(3.0) < 0, f(3.1) < 0 - so not this interval,
f(3.1) < 0 & f(3.2) > 0 - this interval.

So divide up [3.1, 3.2] into ten sub-intervals. Then
f(3.10) < 0 & f(3.11) < 0 - not this interval
f(3.11) < 0 & f(3.12) < 0 - not this interval
f(3.12) < 0 & f(3.13) < 0 - not this interval
f(3.13) < 0 & f(3.14) < 0 - not this interval
f(3.14) < 0 & f(3.15) > 0 -this interval. So, divide up [3.14, 3.15] into ten etc etc...
When do I stop?
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Gregorius
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#13
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#13
(Original post by Mesosleepy)
When do I stop?
When you reach a preset degree of accuracy. This method gives you an extra decimal place for each iteration.
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