Help on conjugate gradient programm in matlab

[hdixa]

hi 1.i have a problem to find the princip to programm in MATLAB the method of conjugate graduate, in fact ,my broblem is:
1.i want to study caracterisque of charge RC WHICH function is :y=a*(1-exp(b*t)) ,a is supposed to be tension maximal and b =1/RC the problem is that i have to find the parametre a and b as we have the equation y=5*(1-exp(-2*t)) + randn(length (t),1); t=1:20 ( 5 et -2 calculate theoriqement)
2. THE traitement has to be by conjugate gradient method.
in summary i have to estimate parametre a and b.

i calculate before a and b by méthode Gauss Newton that's seem great , the broblem in conjugate gradient that i have not a matrix symetrique define positive
thanks for yr help
and sorry for my bad english

 

[NateD]

The conjugate gradient method is an iterative algorithm for solving systems of equations. It works by taking the gradient of a function at a given point and then finding the direction of steepest descent. In this case, the system of equations can be written as y = a*(1-exp(b*t)) where t is a vector of values. To solve this system, you need to find the values of a and b that minimize the difference between the measured data (y) and the model (a*(1-exp(b*t))). This can be achieved through the conjugate gradient method. The conjugate gradient method works by taking the gradient of the error function (the difference between the measured data and the model) at a given point and then finding the direction of steepest descent. In this case, the direction of steepest descent will be in the direction of the parameters a and b. You can then take small steps in this direction and update the parameters accordingly. The method will continue until the error function reaches a minimum. To implement the conjugate gradient method in MATLAB, you will need to define the error function, its gradient, and the step size. Once these have been defined, the algorithm can be implemented in MATLAB using a loop. The loop should start with an initial guess for the parameters a and b, calculate the gradient of the error function at this point, find the direction of steepest descent, take a step in this direction, and update the parameters accordingly. The loop should continue until the error function reaches a minimum or a predefined number of iterations has been reached. Once the loop has finished, the optimized parameters a and b should be returned. I hope this helps.