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Equation solution for large iteration number

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Muhammed Ekin
Muhammed Ekin 2017-11-11
回答： Muhammed Ekin 2017-11-12
Hi everybody,
I have an equation which I need to solve for a large iteration. It takes too many time, I have still waited for it since yesterday to solve.
So is there any solution to solve it faster.
Thank you
for i=1:1:18858
c(i,1)=(a(i,1)/b(i,1));
d(i,1)=(((x+1)*exp(x)))-c(i,1);
y(i,1)=solve(d(i,1),x);
end

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采纳的回答

Roger Stafford
Roger Stafford 2017-11-11
Assuming you have the ‘lambertw’ function on your Matlab system:
d = a./b;
e1 = exp(1);
y = zeros(1,18858);
for ix = 1:1:18858
y(ix) = lambertw(e1*d(ix))-1;
end
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Muhammed Ekin
Muhammed Ekin 2017-11-11
I have already used 'solve' as you see in my question.
Roger Stafford
Roger Stafford 2017-11-11
If you look at “https://www.mathworks.com/help/symbolic/lambertw.html”, you will see that the lambertw function is the solution to the equation
w*exp(w) = k
namely, w = lambertw(k). In your equation, (x+1)*exp(x) = a/b, substitute w = x+1 and get
(x+1)*exp(x) = w*exp(w-1) = w*exp(w)/exp(1) = a/b
Therefore
w*exp(w) = exp(1)*a/b
Consequently
x = w-1 = lambertw(exp(1)*a/b)-1;
There! I've done a 'solve' for you.

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更多回答（1 个）

Muhammed Ekin
Muhammed Ekin 2017-11-12
Thank you although it is slow and give same results to mine, that is another way to solve it.

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