From 0620a19eb9411454bb0c19e6da8982d052982ab5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?J=C3=BCrg=20Lehni?= <juerg@scratchdisk.com>
Date: Sun, 20 Mar 2011 02:01:17 +0000
Subject: [PATCH] Use False Position method as fall back in Newton-Raphson
 method, for accurate results in rare sitatuations wher the fast
 Newton-Raphson method fails.

---
 src/util/Numerical.js | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/util/Numerical.js b/src/util/Numerical.js
index 916c02c0..f6942345 100644
--- a/src/util/Numerical.js
+++ b/src/util/Numerical.js
@@ -74,6 +74,9 @@ var Numerical = new function() {
 			return A * sum;
 		},
 
+		/**
+		 * Newton-Raphson Method Using Derivative
+		 */
 		findRootNewton: function(f, fd, a, b, n, tol) {
 			var x = 0.5 * (a + b);
 			for (var i = 0; i < n; i++) {
@@ -82,7 +85,9 @@ var Numerical = new function() {
 				if (Math.abs(dx) < tol)
 					return x;
 			}
-			return x;
+			// If we did not succeed, fall back on False Position method for
+			// accurate results.
+			return Numerical.findRootFalsePosition(f, a, b, n, tol);
 		},
 
 		findRootFalsePosition: function(f, a, b, n, tol) {