拉格朗日插值多项式在MATLAB中的实现

Hi! 这是我的一个CSDN博客

例

以下给出了针对题（2）的使用方法

输入：
1.节点值
2.需要插值的原函数

对于题（2）需要设置参数为：

xx = [0,0.25,0.5,1];% The nodes(needs to be arranged in order)
y = cos(x)+sin(x); % The function needed to be interpolated

对于题（1）则设置参数为

xx = [0,0.3,0.6];% The nodes(needs to be arranged in order)
y = exp(2*x)*cos(3*x); % The function needed to be interpolated

输出：
1.拉格朗日插值多项式函数 L
2.截断误差限 R

如：
以下是该脚本函数针对题（2）在MATLAB中的输出

The Largrange interpolation polynominal is:
- 0.079318038853536971606466514918676*x^3 - 0.54550876234592496004170044075304*x^2 + 1.006600091875498155701605884745*x + 1.0The Bound of absolute error is:
0.058924941169576826316411910511306*abs(x*(x - 0.25)*(x - 0.5)*(x - 1.0))

具体函数实现

以下拉格朗日插值多项式在MATLAB中的具体实现

// 拉格朗日插值多项式在MATLAB中的具体实现
clear
clc
syms x 
%------------------------------------------------------------
%Variables to be set
xx = [0,0.25,0.5,1];% The nodes（needs to be arranged in order)
y = cos(x)+sin(x); % The function needed to be interpolated
%--------------------------------------------------------------
yy = subs(y,x,xx);
num = length(xx); 
dy = abs(diff(y,num));
l = [];
L = [];
R = [];
for n = 1:numtemp = xx;temp(n) =[];for m = 1:num-1l = [l (x-temp(m))/(xx(n)-temp(m))];end L = [L prod(l)*yy(n)];l = [];
endL = vpa(collect(sum(L),x));
M = eval(max(subs(dy,x,[xx(1):0.01:xx(end)])));
for n = 1:numR = [R x-xx(n)];
end
R = vpa(M/factorial(num)*abs(prod(R)));disp('The Largrange interpolation polynominal is:')
disp(L)
disp('The Bound of absolute error is:')
disp(R)