From 04085a705b27acd9158f4646bf930f31520421b0 Mon Sep 17 00:00:00 2001
From: VaishnavaHari S <cb.en.u4mee16159@cb.students.amrita.edu>
Date: Thu, 11 Oct 2018 14:43:53 +0530
Subject: [PATCH] Add new file
---
divided_difference.m | 48 ++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 48 insertions(+)
create mode 100644 divided_difference.m
diff --git a/divided_difference.m b/divided_difference.m
new file mode 100644
index 0000000..c59a22e
--- /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
--
GitLab