Function Approximation and Interpolation

Question

Sardor Butunboev 2021-10-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1561531-function-approximation-and-interpolation

回答： David Hill 2021-10-11

采纳的回答： David Hill

在 MATLAB Online 中打开

Given: f(x) = exp(-x^2) on the interval [-1; 1].

Need to:

Approximate f(x) by a 9-degree monomial basis polynomial interpolant with equidistant nodes. Proceed as follows:

1.1. create a vector x containing the n = 9 interpolation nodes.

1.2. use the function 'vander' to create the interpolation matrix G.

1.3. compute yi = f(xi) at the n interpolation nodes.

1.4. compute the n basis coefficients c.

2. Evaluate the accuracy of the interpolant, say f1, as follows:

2.1. Use the Matlab function 'polyval' to evaluate f1 for 100 evenly distributed points on [-1; 1].

2.2. Compare these interpolated values with the 'true' values of f.

2.3. Plot the approximation error.

So far, could this. But no idea whether they are correct or not. Don't even understand what should do in 2.2 and 2.3

f = @(x) exp(-x.^2);
n = 9;
y = linspace(-1, 1, n);
z = [];
for i = 1:length(y)
    z(i) = feval(f,y(i));
end
v = fliplr(vander(y));
a = v\z';
b = a(end:-1:1)';
%5
c = linspace(-1,1);
d = polyval(b, c);
p = polyfit(c,d);

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

David Hill 2021-10-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1561531-function-approximation-and-interpolation#answer_806391

在 MATLAB Online 中打开

Something like this.

f = @(x) exp(-x.^2);
x = linspace(-1, 1, 9);
G=vander(x);
y=f(x);
c=G\y';
f1=@(x)polyval(c,x);
t=linspace(-1,1,100);
Error=(f(t)-f1(t))./f(t);
plot(t,Error)