nonlinear equation problem

Hi, I am looking for alpha that solves the following equation. sum(t:1-->N){(a+alpha*Rt)^(-b))*dt}=0 Could any one tell me how can solve it with matlab?

thanks in advance

[Walter Roberson]

What exactly are Rt and dt? Are those R(t) and d(t), two variables indexed at t, or is dt indicating a differentiation, or is it R*t and d*t for known constants R and d ?

[tarik]

Rt and dt are variables dependent on t. t is just an index.

Answer 1

[Walter Roberson]

To check: in MATLAB notation, you are wanting to solve for sum((a+alpha*R).^(-b).*d) being 0 ?

If so, then there is no general solution over the reals.

For example, if b is an even integer, then no matter whether a+alpha*R(t) is positive or negative, the result of raising it to -b will be non-negative. If the d are all positive, you would then be in the situation of having the sum of a series of non-negative numbers be equal to 0. That cannot happen unless you only use one term (in which case alpha = -a/R(1) ) or unless at most one of the R are zero or unless the R are all the same. If you have at least two different non-zero R then at least one of the a+alpha*R(t) terms is going to be positive after raising to -b, leading to a situation that cannot be solved.

If the d have a mix of signs, then for some sets of values there might be a solution even for b being an even integer.