I have a problem of root finding. Format of the function can be arbitrary whereas I want to solve the following one:
f(x)= a+exp(-x**2)(b+c*x+d*x**2)
where a,b,c and d are given parameters, not limited to real numbers. I have read about the root-finding algorithm of polynomial, but still have no idea how to solve functions like I wrote here. Besides the initial guess, how do we determine the value of next iteration based on the former one, and how to find out the conjugate pairs since complex roots are wanted ?
Your function is not a polynomial, because it contains the exponential function. The Newton-Raphson method is often used for numerical root-finding. It is described at length at http://en.wikipedia.org/wiki/Newton%27s_method, with examples.