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Math Help - Need pointer on getting started

  1. #1
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    Need pointer on getting started

    I'm 10 years out of engineering, and haven't really had to use the math part of my education since.

    I have a new problem at work, and I could use a pointer as to where I need to start looking (linear algebra, discrete math?).

    I have an equation of the form

    x[t] = x[t-1]*y[t] / (y[t-1] - y[t])

    For some initial inputs of x and y, this equation becomes harmonic...it repeats every handful of iterations. I would like to develop some guidelines for how to determine what types of data will cause the equation to become harmonic vs. converge to some steady-state value.

    I used to be pretty good with math, just very rusty. I appreciate any advice pointing me in the right direction.

    Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mfeller View Post
    I'm 10 years out of engineering, and haven't really had to use the math part of my education since.

    I have a new problem at work, and I could use a pointer as to where I need to start looking (linear algebra, discrete math?).

    I have an equation of the form

    x[t] = x[t-1]*y[t] / (y[t-1] - y[t])

    For some initial inputs of x and y, this equation becomes harmonic...it repeats every handful of iterations. I would like to develop some guidelines for how to determine what types of data will cause the equation to become harmonic vs. converge to some steady-state value.

    I used to be pretty good with math, just very rusty. I appreciate any advice pointing me in the right direction.

    Thanks!
    This looks like an iterated system, but we have no means of updating the y's. So possibly you will have to post more information (not to mention I am a bit mystified what harmonic would mean if it were an iteration formula).

    CB
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  3. #3
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    More detail

    Hi CB,

    It is an iterative system. I have run into a case where, after ~30 iterations, the next 8 iterations repeat over and over and over...

    Graphing x, it is a waveform.

    Anyway, the first x[t-1] is fixed. If I change it, the particular case that repeats ends up converging, but I have to think that this will result in other cases oscillating instead of converging.

    y is a parabolic function that is determined at the start of the algorithm. x is used to determine what value of y is used. The goal is for the system to converge.

    A little more description

    x[-1] = 1.0;
    m[-1] = 5.0;
    y[-1] = parabolic_lookup_table(m[-1]);

    Loop starting at time 0:
    y[t] = parabolic_lookup_table(m[t-1]);
    x[t] = x[t-1]*y[t] / (y[t-1] - y[t])
    m[t] += x[t]
    Thinking back to a controls class that I had in college, I am wondering if there is a way to quantify stability of the system.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mfeller View Post
    Hi CB,

    It is an iterative system. I have run into a case where, after ~30 iterations, the next 8 iterations repeat over and over and over...

    Graphing x, it is a waveform.

    Anyway, the first x[t-1] is fixed. If I change it, the particular case that repeats ends up converging, but I have to think that this will result in other cases oscillating instead of converging.

    y is a parabolic function that is determined at the start of the algorithm. x is used to determine what value of y is used. The goal is for the system to converge.

    A little more description

    x[-1] = 1.0;
    m[-1] = 5.0;
    y[-1] = parabolic_lookup_table(m[-1]);

    Loop starting at time 0:
    y[t] = parabolic_lookup_table(m[t-1]);
    x[t] = x[t-1]*y[t] / (y[t-1] - y[t])
    m[t] += x[t]
    Thinking back to a controls class that I had in college, I am wondering if there is a way to quantify stability of the system.
    What do you mean by a parabolic look-up table?

    CB
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  5. #5
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    Table

    Sorry...it is a parabolic curve fitted to a data table used when interpolation or extrapolation is needed.
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