拉格朗日插值法

主函数

clear; clc;

x = 0 : 0.1 : 2;

y = sin(x);

x0 = 0.55;

[y0, coef] = Lagrange(x, y, x0);

plot(x, y, 'o-', x0, y0, '*');

子函数

function [y0, coef] = Lagrange(x, y, x0)

%{

函数功能：拉格朗日插值法；

输入：

x：已知点横坐标；

y：已知点纵坐标；

x0：未知点横坐标；

输出：

y0：未知点纵坐标；

coef：插值系数；

%}

% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

if nargin < 3

error('输入参数不足！');

end

m = length(x);

coef = zeros(m, 1);

y0 = 0;

for i = 1 : m

coef(i) = 1;

for j = 1 : m

if j ~= i

coef(i) = coef(i)*(x0 - x(j)) / (x(i) - x(j));

end

end

y0 = y0 + y(i)*coef(i);

end

end