Finding k* which satisfies the equation

Hello all,

I have a question related to finding k* which needs to be a (1X100) vector which satisfies

k* is such that (1-a)*alpha.*theta.*(k+L)^(alpha-1)-((k.^gamma)./w^(1+gamma))=0

where theta and L is (1X100) vectors that is defined and a, alpha and gamma is a number.

[Torsten]

help fzero

Answer 1

[John D'Errico]

It is a really bad idea to want to call a variable k*, since * represents multiplication in MATLAB. gamma is also a poorchoice of variable name, since the gamma function can be a terribly useful one.

As well, you never tell us what w is. Known? Unknown? Scalar? Vector?

I'll assume that w is just a known scalar. If w is unknown, then there is nothing you can do anyway, since the problem would then be unsolvable.

If I assume that w is known as a scalar (even a known vector of elements of the same size as k, this is still no problem) then your problem reduces to a set of scalar problems. So just loop from 1 to 100. Use fzero to solve each sub-problem in turn. Note that a loop here is not inefficient, since fzero is pretty fast, as well as being fairly robust.

I can't help you much more without having some sample data for this variables. If you attach a .mat file containing them, I can look more carefully at the problem. There may be issues with the domain, such as bracketing the solution.

[Mert Demir]

Thank you for your answer. I forget to tell that w is also vector.