Matlab實現——Lagrange approximation

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 lagran.m

%Program 4.1  (Lagrange approximation)

function [C,L]=lagran(X,Y)

%Input  - X is a vector that contains a list of abscissas

%       - Y is a vector that contains a list of ordinates

%Output - C is a matrix that contains the coefficents of

%         the Lagrange interpolatory polynomial

%       - L is a matrix that contains the Lagrange

%         coefficient polynomials

w=length(X); n=w-1; L=zeros(w,w);

%Form the Lagrange coefficient polynomials

for k=1:n+1

   V=1;

   for j=1:n+1

      if k~=j

         V=conv(V,poly(X(j)))/(X(k)-X(j));

      end

   end

   L(k,:)=V;

end

%Determine the coefficients of the Lagrange interpolator polynomial

C=Y*L;

untitled.m

 

X=[0,0.2,0.4,0.6,0.8,1];

Y=[1,2.7183^0.2,2.7183^0.4,2.7183^0.6,2.7183^0.8,2.7183];

[C,L]=lagran(X,Y)

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