Hermite插值matlab代码

以下是Hermite插值的MATLAB代码：

function [y] = Hermite_interp(x, y, dy, xx)
% x: 插值点的x坐标
% y: 插值点的y坐标
% dy: 插值点的导数
% xx: 待插值点的x坐标
% y: 待插值点的y坐标

n = length(x);
m = length(xx);
y = zeros(m,1);

for i = 1:m
    p = 0;
    for j = 1:n
        t = 1;
        for k = 1:n
            if k ~= j
                t = t * (xx(i) - x(k)) / (x(j) - x(k));
            end
        end
        p = p + t * (2*(xx(i) - x(j)) * dy(j) + (1 - 2*(xx(i) - x(j))/(x(j) - x(k)))*y(j));
    end
    y(i) = p;
end

end

调用方法：

% 给定插值点
x = [0, 1, 2];
y = [1, 2, 0];
dy = [0, -1, 4];

% 给定待插值点
xx = linspace(0, 2, 100);

% 使用Hermite插值
yy = Hermite_interp(x, y, dy, xx);

% 绘制插值结果
plot(xx, yy);
hold on;
scatter(x, y);