lagran.m

国外计算机科学教材系列 numerial method using matlab (third edition)

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

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%Upper Saddle River, NJ 07458

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