how to calculate optimal value of a unknown constant of an equation with known data points?

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Hey, I wanted to solve for the optimal value of constant. I have data points of the equation .
please help, how can I do that.
equation is:
y= 1/sqrt(k^2+x^2)

Accepted Answer

Walter Roberson
Walter Roberson on 11 Sep 2020
k0 = rand() * 10;
bestk = lsqcurvefit( @(k,x)1./sqrt(k.^2+x.^2), k0, x, y);
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More Answers (1)

Adam Danz
Adam Danz on 10 Sep 2020
k = sqrt((1/y)^2 - x^2)
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Adam Danz
Adam Danz on 11 Sep 2020
% assign demo values
k = 2.2; % = 2.2
x = 1:10; % = [1,2,3,4,5,6,7,8,9,10]
y = 1./sqrt(k^2 + x.^2); % = [0.41 0.33 0.26 0.21 0.18 0.15 0.13 0.12 0.10 0.09]
% Solve for k
k = sqrt((1./y).^2 - x.^2) % = [2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 ]
k = sqrt((1/y(1))^2 - x(1)^2) % = 2.2
Or, as Walter shows, you can use mean(), mode(), median().

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