Computing error for solution to linear equation

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Tevin 2022-12-19

编辑： John D'Errico 2023-1-8

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?

Matt J 2022-12-19

编辑：Matt J 2022-12-19

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

Tevin 2023-1-8

Should this actually be E=norm(A*x-b) without the square?

John D'Errico 2023-1-8

编辑：John D'Errico 2023-1-8

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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