The sign of t in your inequalities is wrong. Try
A1 = [x,ones(length(y),1),-ones(length(y),1)];
A2 = [-x,-ones(length(y),1),-ones(length(y),1)];
题
I have this MATLAB code and I´m trying to implement the method explained in top answer of this question: https://stats.stackexchange.com/questions/12546/software-package-to-solve-l-infinity-norm-linear-regression Here is the code that I´m using that starts with the data points:
x = [
0
0.101010101010101
0.202020202020202
0.303030303030303
0.404040404040404
0.505050505050505
0.606060606060606
0.707070707070707
0.808080808080808
0.909090909090909
];
y = [
0.052993311292562
14.923120014175920
1.974502763975613
-2.205773310050583
-0.052548781318830
2.935428041987883
0.134606520161892
0.146742215922384
-0.418386565682831
1.702041272689124
];
A1 = [x,ones(length(y),1),-ones(length(y),1)];
A2 = [-x,-ones(length(y),1),-ones(length(y),1)];
A = [A1;A2];
f = [0;0;1];
linprog(f,A,[y;-y])
The point is to find the the parameters (slope and intersection) of the best fit, i.e. a line, by minimizing the L-infinity norm of the residuals between the line and data points. I have made the same problem work for ordinary least squares (minimizing the L-2 norm) as well as for the L-1 fit. The line plotted from those methods fit really nicely between the data points. But can't seem to make this L-infinity fit work no matter what I do so I come to you for help, any tips appreciated.
解决方案
The sign of t in your inequalities is wrong. Try
A1 = [x,ones(length(y),1),-ones(length(y),1)];
A2 = [-x,-ones(length(y),1),-ones(length(y),1)];