diff --git a/divided_difference.m b/divided_difference.m new file mode 100644 index 0000000000000000000000000000000000000000..c59a22e00fd1cbd113bf31c7f19cc19f91b48e0c --- /dev/null +++ b/divided_difference.m @@ -0,0 +1,48 @@ +function TDD = divided_difference(X, Y) +% +% TDD = divdiff(X, Y) +% +% DIVDIFF +% Newton's Method for Divided Differences. +% +% The following formula is solved: +% Pn(x) = f(x0) + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... +% + f[x0,x1,..,xn](x-x0)(x-x1)..(x-x[n-1]) +% where f[x0,x1] = (f(x1-f(x0))/(x1-x0) +% f[x0,x1,..,xn] = (f[x1,..,xn]-f[x0,..,x_[n-1]])/(xn-x0) +% +% NOTE: f^(n+1)(csi)/(n+1)! aprox. = f[x0,x1,..,xn,x_[n+1]] +% +% Input:: +% X = [ x0 x1 .. xn ] - object vector +% Y = [ y0 y1 .. yn ] - image vector +% +% Output: +% TDD - table of divided differences +% +% Example: +% TDD = divdiff( [ 1.35 1.37 1.40 1.45 ], [ .1303 .1367 .1461 .1614 ]) +% +% Author: Tashi Ravach +% Version: 1.0 +% Date: 22/05/2006 +% + + if nargin ~= 2 + error('divdiff: invalid input parameters'); + end + + [ p, m ] = size(X); % m points, polynomial order <= m-1 + if p ~= 1 || p ~=size(Y, 1) || m ~= size(Y, 2) + error('divdiff: input vectors must have the same dimension'); + end + + TDD = zeros(m, m); + TDD(:, 1) = Y'; + for j = 2 : m + for i = 1 : (m - j + 1) + TDD(i,j) = (TDD(i + 1, j - 1) - TDD(i, j - 1)) / (X(i + j - 1) - X(i)); + end + end + +end