Minimizing linear equation Ax=b using gradient descent

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Tevin 2022-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/1881797-minimizing-linear-equation-ax-b-using-gradient-descent

评论： Tevin 2022-12-20

采纳的回答： Matt J

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 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 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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采纳的回答

Matt J 2022-12-20

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编辑：Matt J 2022-12-20

在 MATLAB Online 中打开

[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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Torsten 2022-12-20

It's sqrt(sum((A*x-b).^2))

Tevin 2022-12-20

Thank you both. This really helped

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