Computing error for solution to linear equation

2022 12 19
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更新时间：2023 1 8
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I want to solve a linear equation Ax= b, using least-squares. I also need to find the error in the solution. I am not sure how to find the error.
Error is;
𝐸=‖𝐴𝒙−𝒃‖^2 =Σ𝜃𝑖^2 where i is index counter
A=[2 0;3 1;4 3];
b=[2;3;4];
x= A\b;
I am not sure how to calculate the error. Can someone help me?

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Matt J
Matt J 2022-12-19
编辑：Matt J 2022-12-19

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x= A\b;
E=norm(A*x-b)^2

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Tevin
Tevin 2023-1-8
Should this actually be E=norm(A*x-b) without the square?
John D'Errico
John D'Errico 2023-1-8
编辑：John D'Errico 2023-1-8
@Tevin
NO, it should not be.
What was asked for? In your own question, you showed the norm(A*x-b) SQUARED. @Matt J gave you the square of the norm.
It can be whatever you want, but if you want something else, then it is you who needs to make the decision.

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