拉格朗日插值多项式及Matlab代码

拉格朗日多项式为

()()0n

n k k k L x y l x ==∑

式中

()()()()()()()()()

011011k k n k k k k k k k n x x x x x x x x l x x x x x x x x x -+-+----=---- 给定函数表如下

1）取010.2,0.3x x ==计算0.285e 的近似值

2）取0120.2,0.3,0.4x x x ===计算0.285e 的近似值 function LagrangeSpline

x0=[0.1,0.2,0.3,0.4,0.5];

y0=[1.1052,1.2214,1.3499,1.4918,1.6487]; xq=0.285;

x=x0(2:4);

y=y0(2:4);

yq=LagrangePoly(x,y,xq)

return ;

function yq=LagrangePoly(x,y,xq)

xnum=length(x);ynum=length(y);

if xnum==ynum

for k=1:xnum

H1(k,:)=xq-x;

H1(k,k)=1;

H2(k,:)=x(k)-x;

H2(k,k)=1;

end ;

L=prod(H1,2)./prod(H2,2);

end ;

yq=sum(L'.*y);

return ;