Polynomial Approximation, is it possible in matlab?
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I have four points on the graph with the following coordinates.
x1 - 1
y1 - 3.5
x2 - 2
y2 - 14/3
x3 - 3
y3 - 14
x4 - 4
y4 - 28
Is it possible using the Lagrange approximation polynomial coefficient calculation method to find the polynomial / function given by the four points?
I don't know the algorithm very well and I don't have the strongest matlab knowledge. I'm learning.
Thank you.
MATLAB Version: 8.5.0.197613 (R2015a)
回答（1 个）
Hi,
Try below (it uses least squares):
For lagrange you can look at that link:
x1 = 1;
y1 = 3.5;
x2 = 2;
y2 = 14/3;
x3 = 3;
y3 = 14;
x4 = 4;
y4 = 28;
x1Array = [x1,x2,x3,x4];
y1Array = [y1,y2,y3,y4];
n = 1; % polynomial degree (you can change it as you wish)
p = polyfit(x1Array,y1Array,n); % p is coefficient of your polynomial: P(X) = P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1) descending order.
newY = polyval(p,x1Array); % function results
plot(x1Array,y1Array, 'bo',x1Array,newY,'-r');
grid;
legend('Data','Fitted Data');
11 个评论
Milky Way
2019-1-4
Ok. But where is the function, the polynomial. When I run the program I only show a graph.
madhan ravi
2019-1-4
编辑：madhan ravi
2019-1-4
reduce n less than 4
Milky Way
2019-1-4
Okay. But how can I find the polynomial? Simple form: aX^n + bX^(n-1) .... the polynomial itself.
Steven Lord
2019-1-4
See the comment on line 12.
Torsten
2019-1-4
p(x)=(x-x2)*(x-x3)*(x-x4)/((x1-x2)*(x1-x3)*(x1-x4))*y1+...
(x-x1)*(x-x3)*(x-x4)/((x2-x1)*(x2-x3)*(x2-x4))*y2+...
(x-x1)*(x-x2)*(x-x4)/((x3-x1)*(x3-x2)*(x3-x4))*y3+...
(x-x1)*(x-x2)*(x-x3)/((x4-x1)*(x4-x2)*(x4-x3))*y4
Multiply out and order according to powers of x.
Milky Way
2019-1-4
Torsten
2019-1-4
Yes, the coefficients can be taken from the line
p = polyfit(x1Array,y1Array,n); % p is coefficient of your polynomial: P(X) = P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1) descending order.
of your above code.
Milky Way
2019-1-4
Yes. Thank you very much, I'm at the beginning, but as I said, I'll learn. :)
Torsten
2019-1-4
But you know that using the interpolating spline method to calculate the coefficients is not what you are supposed to do in your homework (it says something about "Lagrange interpolation polynomial", doesn't it) ??
Luna
2019-1-4
Yes, it says lagrange that's why I gave the lagrangepoly link from fileexchange in my answer.
Please check the file and use. It does the same thing with only Lagrange method.
It also explains with examples.
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