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    How to do decimal search

    Also, is there a quicker way to do it?
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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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    (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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    (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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    (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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    (Original post by TeeEm)
    sorry but I am teaching at the moment
    Fair enough, sorry to disturb
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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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    (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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    (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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    (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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    (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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    (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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