# Condtion of an equation

1. Aug 12, 2011

### hermano

Condition of an equation

Hi,

I have an equation (transfer function) which I must calculate for several harmonics 'k' (from 1 till 100) namely:

H(k) = 1 + a * exp(i*k*alpha) + b * exp(i*k*beta)

Depending on the variables (a, b, alpha, beta), H(k) becomes zero or almost zero depending on the value of k. Because this undesired for my problem (I devide by this H(k), thus the result can go to infinity), I want to do an optimisation to search for the best variables (a, b, alpha, beta) in such a way that the values of H(k), for k 1 till 100, are not in the vicinity of zero. I want to give a score on each value of H(k) depending of the value reaches zero or not, a sort of condition number, which I sum in the end for each value of H(k). Depending on the value of the condition number I can make then a choice which variables are most appropriate.

Can anybody help me how I can define such a condition number for this problem?

Thanks

Last edited: Aug 12, 2011