How to minimize the maximum error?
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Good day everyone,
I have this pack of data that are functions of three variables (say, x1, x2 and x3). How do I choose a linear approximating function that minimizes the maximum error between the linear function and the data? I'm getting some approximating functions with an other software that cannot provide this specific detail to choose between them, though, so I'm quite stuck.
On the other hand I've been suggested to use fminimax in MatLab, but it doesn't seem to be usable in this case (to me, and I'm not a "so experienced user" so I may be wrong).
Thank you so much in advance!
Stefano
采纳的回答
By a "linear approximating function" you mean a function l with
l(x1,x2,x3) = a + b*x1 + c*x2 + d*x3
where a, b, c and d are constants that have to be determined as to minimize the maximum of
abs(a + b*x1 + c*x2 + d*x3 - y)
?
Use "linprog" to solve the optimization problem
min: t
s.c.
a + b*x1 + c*x2 + d*x3 - y <= t
a + b*x1 + c*x2 + d*x3 - y >= -t
更多回答（1 个）
Example:
rng('default')
n = 100;
x1 = rand(n,1);
x2 = rand(n,1);
x3 = rand(n,1);
y = rand(n,1);
f = [1; 0 ;0; 0; 0];
A = [-ones(n,1),ones(n,1),x1,x2,x3;-ones(n,1),-ones(n,1),-x1,-x2,-x3];
b = [y;-y];
[sol,fval] = linprog(f,A,b)
t = sol(1)
a = sol(2)
b = sol(3)
c = sol(4)
d = sol(5)
3 个评论
Stefano Gilardoni
2023-6-8
Stefano Gilardoni
2023-6-8
Torsten
2023-6-8
Instead of
x1 = rand(n,1);
x2 = rand(n,1);
x3 = rand(n,1);
y = rand(n,1);
you just have to supply your data as column vectors.
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