?? lagrange3ci.txt
字號:
PRE class=m name="code">% 分段三次Lagrange插值
% 命令格式:y=lagrange3(x0,y0,x)
% x0為節(jié)點向量,y0為對應的函數(shù)值向量,
% x為插值點向量,返回值y為x處的函數(shù)近似值向量。
function y=lagrange3(x0,y0,x)
[n1,n]=size(x0);
[n1,m]=size(x);
for i=1:m
u=x(i);
if u<=x0(3)
y(i)=y0(1)*(u-x0(2))*(u-x0(3))*(u-x0(4))/(x0(1)-x0(2))/(x0(1)-x0(3))/(x0(1)-x0(4))+...
y0(2)*(u-x0(1))*(u-x0(3))*(u-x0(4))/(x0(2)-x0(1))/(x0(2)-x0(3))/(x0(2)-x0(4))+...
y0(3)*(u-x0(1))*(u-x0(2))*(u-x0(4))/(x0(3)-x0(1))/(x0(3)-x0(2))*(x0(3)-x0(4))+...
y0(4)*(u-x0(1))*(u-x0(2))*(u-x0(3))/(x0(4)-x0(1))/(x0(4)-x0(2))*(x0(4)-x0(3));
elseif u>=x0(n-2)
y(i)=y0(n-3)*(u-x0(n-2))*(u-x0(n-1))*(u-x0(n))/(x0(n-3)-x0(n-2))/(x0(n-3)-x0(n-1))/(x0(n-3)-x0(n))+...
y0(n-2)*(u-x0(n-3))*(u-x0(n-1))*(u-x0(n))/(x0(n-2)-x0(n-3))/(x0(n-2)-x0(n-1))/(x0(n-2)-x0(n))+...
y0(n-1)*(u-x0(n-3))*(u-x0(n-2))*(u-x0(n))/(x0(n-1)-x0(n-3))/(x0(n-1)-x0(n-2))/(x0(n-1)-x0(n))+...
y0(n)*(u-x0(n-3))*(u-x0(n-2))*(u-x0(n-1))/(x0(n)-x0(n-3))/(x0(n)-x0(n-2))/(x0(n)-x0(n-1));
else
for k=3:n-2
if u>x0(k) & u<=x0(k+1)
y(i)=y0(k-1)*(u-x0(k))*(u-x0(k+1))*(u-x0(k+2))/(x0(k-1)-x0(k))/(x0(k-1)-x0(k+1))/(x0(k-1)-x0(k+2))+...
y0(k)*(u-x0(k-1))*(u-x0(k+1))*(u-x0(k+2))/(x0(k)-x0(k-1))/(x0(k)-x0(k+1))/(x0(k)-x0(k+2))+...
y0(k+1)*(u-x0(k-1))*(u-x0(k))*(u-x0(k+2))/(x0(k+1)-x0(k-1))/(x0(k+1)-x0(k))/(x0(k+1)-x0(k+2))+...
y0(k+2)*(u-x0(k-1))*(u-x0(k))*(u-x0(k+1))/(x0(k+2)-x0(k-1))/(x0(k+2)-x0(k))/(x0(k+2)-x0(k+1));
end
end
end
end
y;
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