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Hello guys,

thanks for looking over here!

I'd like to ask about Newton's method in the MATLAB, I have seen many questions about the newton's method in the forum, while I have tried to apply those in my code but it seems that something goes wrong and I spent a lot of time trying to figure what's going on. HereI attached my code, I appreicate if you can help me to figure it out.

Thanks in advance again!

This is what I have wrote:

clear all

close all

u0 = inf; % x0 initial point

h1 = 1; % constant in the equation

E = 25; % constant in the equation

Number = 10; %N

tol = 1e-10;

u(1) = u0;

n = 2;

nfinal = Number+1;

Dm = 10; % constant in the equation

N = 10; % constant in the equation

P1 = (E - (abs(h1).^2).* (exp(N./Dm)-1).* u.^-1)./(Dm + u.^-1);

P2 = (E + (abs(h1).^2).* (exp(N./Dm)-1).* Dm)./(Dm + u.^-1);

A = log2(1+(abs(h1).^2).*P2);

B = N - Dm.* log2(1+exp(-N./Dm).*P1.*abs(h1).^2);

F = A - u.*B; %% equation of the function

while(n<= Number + 1)

Fe = F(u(n-1));

Be = B(u(n-1));

u(n) = u(n-1) + Fe./(Be-(E+Dm.*(exp(N/Dm)-1))/(exp(N/Dm).*Dm.*u+E.*u + 1));

Tn(n) = 1/u(n);

if(abs(Fe)<= tol)

nfinal = n;

break;

end

n = n+1;

end

delay_minimize = Dm + Tn;

plot(0:nfinal-1,delay_minimize)

%%end of the code

What goes wrong is that in the line:

Fe = F(u(n-1));

The MATLAB gives me that the index has to be positve integer or logical value. But I already set n to the 2, I don't really know what's going on.

Btw, the reason for I didn't use diff function is that the F'(u) is equal to the equation I put in the while loop which is : (Be-(E+Dm.*(exp(N/Dm)-1))/(exp(N/Dm).*Dm.*u+E.*u + 1)); and the requirement of the the initial point has to be inf.

Thank you! have a good day!

Steven Lord
on 15 Feb 2020

As you've written your code F isn't a function. It's a numeric array. That means F(u(n-1)) is an attempt to get whatever is in element u(n-1) of F.

You probably want to specify your function as an anonymous function (if it's simple enough) or as a function handle to a function written in a file (if it's more complicated.) Search the documentation for "anonymous function" or "function handle" for more information.

F = @(u) someExpressionDependingOnTheVariableu

You will need to fill in what "someExpressionDependingOnTheVariableu" is. You'll also need to do the same thing for B.

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