Add the divided_difference_coefficients() function and reimplement divided_difference...

[octave.git] / divided_difference.m

diff --git a/divided_difference.m b/divided_difference.m
index 2b8f8df0d5e75ca126b618acb8e81257235e79c2..a9039b10c042caa773c4b162f0d6ee94e95734fe 100644 (file)
--- a/divided_difference.m
+++ b/divided_difference.m
@@ -15,7 +15,7 @@ function dd = divided_difference(f, xs)
   ## OUTPUTS:
   ##
   ##   * ``dd`` - The divided difference f[xs(1), xs(2),...]
-  ##
+  ## 
   order = length(xs) - 1;
   
   if (order < 0)
@@ -25,14 +25,8 @@ function dd = divided_difference(f, xs)
     ## Our base case.
     dd = f(xs(1))
   else
-    ## Order >= 1, recurse.
-
-    ## f[x0,...,x_n-1]
-    f0 = divided_difference(f, xs(1:end-1));
-    ## f[x1,...,x_n]
-    f1 = divided_difference(f, xs(2:end));
-
-    # http://mathworld.wolfram.com/DividedDifference.html
-    dd = (f0 - f1)/(xs(1) - xs(end));
+    ## Order >= 1.
+    cs = divided_difference_coefficients(xs)
+    dd = dot(cs, f(xs));
   end
 end