Minimizing linear equation Ax=b using gradient descent

Tevin

2022 12 20

1 个回答

回答已采纳

7 次查看（30 天）

0 个投票

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.

4 个评论
显示 2更早的评论隐藏 2更早的评论

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.

请先登录，再进行评论。

请先登录，再回答此问题。

Follow Question

采纳的回答

Matt J 2022-12-20

编辑：Matt J 2022-12-20

在 MATLAB Online 中打开

0 个投票

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

3 个评论
显示 1更早的评论隐藏 1更早的评论

Torsten 2022-12-20

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

Tevin 2022-12-20

Thank you both. This really helped

请先登录，再进行评论。

Minimizing linear equation Ax=b using gradient descent

4 个评论
显示 2更早的评论隐藏 2更早的评论

采纳的回答

3 个评论
显示 1更早的评论隐藏 1更早的评论

更多回答（0 个）

类别

标签

Community Treasure Hunt

Minimizing linear equation Ax=b using gradient descent

4 个评论 显示 2更早的评论 隐藏 2更早的评论

采纳的回答

3 个评论 显示 1更早的评论 隐藏 1更早的评论

更多回答（0 个）

类别

标签

另请参阅

Community Treasure Hunt

4 个评论
显示 2更早的评论隐藏 2更早的评论

3 个评论
显示 1更早的评论隐藏 1更早的评论