- never ever use ^(-1) or inv to solve a linear system. Backslash operator is faster and more accurate.
- the transpose operator is .' for the transpose. A simple ' is the complex conjugate transpose. In your case this is not affecting the result, but it is a good practice to keep the two operations separated.
- Note that you can solve the least-square problem without explicitly write the normal equations using the backslash operator on your overdetermined system

# How can I calculate the sum of the absolute error?

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Hello,

I am trying to do some exercises in Matlab, and i have trouble with calculating the absolute error and state it with 2 decimal places. You can see the exercise (the last one) in the image below.

I am done with sub task 1 and 2, where i got:

A_system_matrix = [1 -2 3; 1 -1 0; 1 0 -1; 1 1 0; 1 2 3] % System matrix A

y_vector = [0; 15; 25; 50; 110]

rref([A'*A,A'*y_vector]) % Using rowreducing

(A'*A)^(-1)*A'*y_vector % Using the equation stated in the text above

Can someone help me with using Matlab to calculate the sum of the absolute error stated in the exercise and then state it with 2 decimal places?

Thanks a lot!

##### 0 Comments

### Accepted Answer

Fabio Freschi
on 23 Sep 2021

Edited: Fabio Freschi
on 23 Sep 2021

Please check the code below.

clear all, close all

% model

F = @(c,x)c(1)+c(2)*x+c(3)*(x.^2-1);

% data

xk = [-2 -1 0 1 2].';

yk = [0 15 25 50 110].';

% build matrix A

A = [F([1 0 0],xk) F([0 1 0],xk) F([0 0 1],xk)];

% least-square fit

c = (A.'*A)\(A.'*yk);

% error

err = sum(abs(yk-F(c,xk)));

fprintf('error = %.2f\n',err);

% plot

x = (-2:.1:2).';

figure, hold on

plot(xk,yk,'o')

plot(x,F(c,x))

Three remarks

c = A\yk;

##### 3 Comments

Fabio Freschi
on 23 Sep 2021

Edited: Fabio Freschi
on 23 Sep 2021

Decimal places means digits after the decimal point.

The error formula in your OP is a scalar, so you should produce only one number

If my answer solves your problem, please accept it

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