牛顿插值法matlab
时间: 2023-10-16 07:09:45 浏览: 46
以下是一个使用牛顿插值法的 MATLAB 代码示例:
function [p] = newton_interpolation(x, y, xi)
% x: known data points x values
% y: known data points y values
% xi: interpolation points x values
% p: interpolation points y values
n = length(x);
b = zeros(n, n);
% initialize the first column of b with y values
for i = 1:n
b(i, 1) = y(i);
end
% construct the rest of b using divided differences
for j = 2:n
for i = j:n
b(i, j) = (b(i, j-1) - b(i-1, j-1)) / (x(i) - x(i-j+1));
end
end
% evaluate the polynomial at xi
p = zeros(size(xi));
for i = 1:length(xi)
s = b(1, 1);
for j = 2:n
prod = 1;
for k = 1:j-1
prod = prod * (xi(i) - x(k));
end
s = s + b(j, j) * prod;
end
p(i) = s;
end
end
你可以将此代码保存为一个名为“newton_interpolation.m”的函数文件,并在 MATLAB 中调用它。下面是一个示例用法:
x = [0 1 2];
y = [1 4 3];
xi = 0:0.1:2;
p = newton_interpolation(x, y, xi);
plot(x, y, 'o', xi, p, '-')