newpoly.m

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

function [C,D]=newpoly(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 vector that contains the coefficients
%          of the Newton intepolatory polynomial
%        - D is the divided difference table

% 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

n=length(X);
D=zeros(n,n);
D(:,1)=Y';

%Use formula (20) to form the divided difference table

for j=2:n
   for k=j:n
      D(k,j)=(D(k,j-1)-D(k-1,j-1))/(X(k)-X(k-j+1));
   end
end

%Determine the coefficients of the Newton interpolatory polynomial

C=D(n,n);

for k=(n-1):-1:1
   C=conv(C,poly(X(k)));
   m=length(C);
   C(m)=C(m)+D(k,k);
end