finding a coefficient from an equation
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Hello, i m a beginner on matlab and i would need some help. I have 2 vectors x and z with 10 values each and the equation z=c*sqrt(x). I have to find the value of c. Help please.
3 个评论
Adam Danz
2020-5-18
This is more of a math problem than a Matlab problem.
In essence, you have to solve for c. Then you just have to plug in your vectors.
Since this is likely homework, I'd be glad to help you solve.
Hint #1:
y = x*A ---> y/A = x
Hint #2:
To divide two vectors element-wise, use q./r
Ana Monea
2020-5-18
Walter Roberson
2020-5-18
In that case either use / or \ operators with appropriate arguments. They will do a least-squared fitting to find the best value for c.
回答（1 个）
Ang Feng
2020-5-18
(1)If your vectors x and x follows exactly z=c*sqrt(x), then the constant c can be calculated, as mentioned by Adam Danz,
c = sqrt(x)./z
You have a vector c which has 10 identical value which is what you are looking for.
(2) In the case x, and z just follow then trend of z=c*sqrt(x), you are actually asking for a constant c that minimize some function of the error
vector. Normally, we minimize norm of the square of the error 
. This is a least square problem. You can actually use the curve fitting tool box to fit the function.
vector. Normally, we minimize norm of the square of the error . This is a least square problem. You can actually use the curve fitting tool box to fit the function.sqrtX = sqrt(x);
f = fit(sqrtX,z,'poly1');
c = f.p1;
Here is my little example.
x = (1:10)';sqrtX = sqrt(x);
z = 2*sqrtX+0.05*randn(10,1);% add some noise
f = fit(sqrtX,z,'poly1');
c = f.p1
ans =
1.9725
The parameter c = 2 was calculated to be 1.9725.
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