Mote Carlo Method: Characteristic Function Required
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I require MATLAB to generate a random set of functions that will meet all those conditions. Is MATLAB able to do that? The requirements of the function, say f(t) for 0 < t < t_max, is:
- f(0) = 0
- f(t_max) = 0
- Global min >= 0 % all values >0
- f ' (t)_max <= b % known value of b
- f ' (t)_min >= -b
- integral[f(t)] = c % known value of c
I would like MATLAB to generate a function (Fourier series or n-degree polynomial) that meet all those conditions.
If it is too lengthy to explain the process/math involved/MATLAB functions available to do so, I kindly request you point me in the right direction.
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Walter Roberson
2011-7-29
Depending on the relationships between a, b, and c, a simple 1/2 * c * sin(t*Pi/t_max) might do.
Your last two conditions are, by the way, redundant because of your 5th and 6th conditions.
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Walter Roberson
2011-7-30
That would have been useful information to have known before I spent time on this.
I am not at the moment convinced that it can be done by a finite polynomial, but I would need to work at it further. The people over on mathhelpforum are probably much better skilled at this kind of work than I am.
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