From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 25 Sep 2012 14:25:52 +0000 (-0400)
Subject: Add Newton's method tests.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=194f00d6448219fe1208ad59af136fbf67c863b5

Add Newton's method tests.
---

diff --git a/src/Roots/Simple.hs b/src/Roots/Simple.hs
index 2689163..0b0b93d 100644
--- a/src/Roots/Simple.hs
+++ b/src/Roots/Simple.hs
@@ -77,6 +77,15 @@ bisect f a b epsilon =
 
 -- | The sequence x_{n} of values obtained by applying Newton's method
 --   on the function @f@ and initial guess @x0@.
+--
+--   Examples:
+--
+--   Atkinson, p. 60.
+--   >>> let f x = x^6 - x - 1
+--   >>> let f' x = 6*x^5 - 1
+--   >>> tail $ take 4 $ newton_iterations f f' 2
+--   [1.6806282722513088,1.4307389882390624,1.2549709561094362]
+--
 newton_iterations :: (Fractional a, Ord a)
                     => (a -> a) -- ^ The function @f@ whose root we seek
                     -> (a -> a) -- ^ The derivative of @f@
@@ -92,6 +101,19 @@ newton_iterations f f' x0 =
 
 -- | Use Newton's method to find a root of @f@ near the initial guess
 --   @x0@. If your guess is bad, this will recurse forever!
+--
+--   Examples:
+--
+--   Atkinson, p. 60.
+--
+--   >>> let f x = x^6 - x - 1
+--   >>> let f' x = 6*x^5 - 1
+--   >>> let Just root = newtons_method f f' (1/1000000) 2
+--   >>> root
+--   1.1347241385002211
+--   >>> abs (f root) < 1/100000
+--   True
+--
 newtons_method :: (Fractional a, Ord a)
                  => (a -> a) -- ^ The function @f@ whose root we seek
                  -> (a -> a) -- ^ The derivative of @f@