Mote Carlo Method: Characteristic Function Required

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.

Answer 1

[John]

The required function first needs a more comprehensive method of being defined before the process to do so can be discussed here.

Answer 2

[Walter Roberson]

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.

[John]

Yes I realise.

I am trying to use MATLAB to generate a random set of functions that will meet all those conditions. Is MATLAB able to do that?

For more details on the function see (http://www.mathhelpforum.com/math-help/f6/monte-carlos-method-particular-equation-style-required-185291.html#post669552).

[Walter Roberson]

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.