How to fit a smooth curve on discrete data.

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Raj Arora
Raj Arora 2022-10-19
编辑： Torsten 2022-10-20
Hello all, I want to produce an equation that can develop a continous smooth curve (does not matter whether it follow any distribution or any plot) which connect the data given below. Using that equation I can interpolate data in between but I want a smoooth curve not a discrete curve. Can anyone please help me with this.
x = [3, 2.5, 2, 1.5, 1, 0.5]
y = [1.8, 1.75, 1.71, 1.55, 0.8, 1.25]
plot(x,y)

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Torsten
Torsten 2022-10-19
Ran in:
Maybe something like this:
x = [3, 2.5, 2, 1.5, 1, 0.5];
y = [1.8, 1.75, 1.71, 1.55, 0.8, 1.25];
plot(x,y)
xx = linspace(x(1),x(end),100);
yy = interp1(x,y,xx,'cubic');
hold on
plot(xx,yy)
hold off
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Raj Arora
Raj Arora 2022-10-20
Alex can you tell me the procedure how you come up with this equaiton and values of p1 p2 p3 p4?
Torsten
Torsten 2022-10-20
编辑：Torsten 2022-10-20
Ran in:
Alex's idea is to approximate your data by a curve. This curve does not pass exactly through each of your data points, but gives a good approximation over the complete interval with a small number of coefficients.
x = [3, 2.5, 2, 1.5, 1, 0.5];
y = [1.8, 1.75, 1.71, 1.55, 0.8, 1.25];
fun = @(p,x) p(1)./(p(2)+(x-p(3)).^2)+p(4) ;
fun1 = @(p) fun(p,x)-y;
p0 = [-0.1;0.1;0.9;2] ;
sol = lsqnonlin(fun1,p0)
Local minimum possible. lsqnonlin stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.
sol = 4×1
-0.1412 0.1199 0.8609 1.8143
hold on
plot(x,y,'o')
xx = x(1):-0.01:x(end);
plot(xx,fun(sol,xx))
hold off

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