Minimizing linear equation Ax=b using gradient descent

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Tevin
Tevin 2022-12-20
评论： Tevin 2022-12-20
I want to find the error in the solution to Ax=b, using gradient descent.
E=||Ax-b||^2
x = [x1;x2], where x1 and x2 range between -5 and 5, with step size 0.2 for each direction.
How do I use Gradient Descent to search for a local minimum with know step size of 0.2, learning rate= 0.1. The search should stop when the difference between previous and current value is 0.002. I am to find solution for x using Gradient Descent, as well error E.
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Hiro Yoshino
Hiro Yoshino 2022-12-20
You need to derive the derivative of the Error function. Gradient Descent requires it to move the point of interest to the next.
Tevin
Tevin 2022-12-20
Thank you. The function that I wrote already does that. My problem is that I struggle to calculate error for all the grid values (X,Y). The array sizes are incompatible but I am not sure how to fix that.

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Matt J
Matt J 2022-12-20
编辑：Matt J 2022-12-20
[X1,X2]= meshgrid(-5:0.2:5);
x=[X1(:)';X2(:)'];
E=vecnorm( A*x-b, 2,1);
E=reshape(E,size(X1)); %if desired

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