牛顿插值 | MATLAB源码

%% 
% 此代码解决了，利用牛顿差值公式，已知 $sin(0.2) \sin(0.3) \sin(0.4)  \sin(0.5)  \sin(0.6)  \sin(0.7)$的情况下，对 
% $\sin(0.55)$ 的差值估计。

clc,clear,close all
%%
% 主程序 | 输入已知量，估计未知量
x_train = [0.2 0.3 0.4 0.5 0.6 0.7];%注意，这里 x_train 应该输入一个行向量
y_train = sin(x_train);
x_test = 0.55;
y_test = myfun(x_test,x_train,y_train)
y_real = sin(0.55)
%% 
% 牛顿差值的函数

function y_test=myfun(x_test,x_train,y_train)
x_train=x_train';y_train=y_train';
n = length(x_train);
total_diff = zeros(n);
total_diff(:,1) = y_train;
for i = 2:n
    total_diff(:,i) = (total_diff(:,i-1)-total_diff(i-1,i-1))./(x_train-x_train(i-1));
end
% total_diff 表示的是各阶均差，注意：主对角线以上的（不包括主对角线）上的数据请忽略。
a = diag(total_diff);
y_test = 0;
for i = 1:n
    r = a(i);
    for j = 1:i
        if j~=1
            r = r*(x_test-x_train(j-1));
        end
    end
    % 利用刚刚计算得到的系数a，得到y_test的估计值
    y_test = y_test + r;
end
end

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2021年9月23日15:37:51