# Boost-Commit :

From: pbristow_at_[hidden]
Date: 2007-08-22 09:17:06

Author: pbristow
Date: 2007-08-22 09:17:04 EDT (Wed, 22 Aug 2007)
New Revision: 38840
URL: http://svn.boost.org/trac/boost/changeset/38840

Log:
PUnctuation
Text files modified:
sandbox/math_toolkit/libs/math/doc/roots_without_derivatives.qbk | 10 +++++-----
1 files changed, 5 insertions(+), 5 deletions(-)

Modified: sandbox/math_toolkit/libs/math/doc/roots_without_derivatives.qbk
==============================================================================
--- sandbox/math_toolkit/libs/math/doc/roots_without_derivatives.qbk (original)
+++ sandbox/math_toolkit/libs/math/doc/roots_without_derivatives.qbk 2007-08-22 09:17:04 EDT (Wed, 22 Aug 2007)
@@ -117,14 +117,14 @@

Alternatively, there is a simple bisection routine which can be useful
in its own right in some situations, or alternatively for narrowing
-down the range containing the root prior to calling a more advanced
+down the range containing the root, prior to calling a more advanced
algorithm.

All the algorithms in this section reduce the diameter of the enclosing
interval with the same asymptotic efficiency with which they locate the
root. This is in contrast to the derivative based methods which may /never/
significantly reduce the enclosing interval, even though they rapidly approach
-the root. This is also in contrast to some other derivate free methods
+the root. This is also in contrast to some other derivative-free methods
(for example the methods of [@http://en.wikipedia.org/wiki/Brent%27s_method Brent or Dekker)]
which only reduce the enclosing interval on the final step.
Therefore these methods return a std::pair containing the enclosing interval found,
@@ -194,7 +194,7 @@

where /m/ is the initial value of /max_iter/ passed to the function.

-In other words it's up to the caller to verify whether termination occurred
+In other words, it's up to the caller to verify whether termination occurred
as a result of exceeding /max_iter/ function invocations (easily done by
checking the value of /max_iter/ when the function returns), rather than
because the termination condition /tol/ was satisfied.
@@ -261,7 +261,7 @@

where /m/ is the initial value of /max_iter/ passed to the function.

-In other words it's up to the caller to verify whether termination occurred
+In other words, it's up to the caller to verify whether termination occurred
as a result of exceeding /max_iter/ function invocations (easily done by
checking the value of /max_iter/ when the function returns), rather than
because the termination condition /tol/ was satisfied.
@@ -347,7 +347,7 @@

where /m/ is the initial value of /max_iter/ passed to the function.

-In other words it's up to the caller to verify whether termination occurred
+In other words, it's up to the caller to verify whether termination occurred
as a result of exceeding /max_iter/ function invocations (easily done by
checking the value of /max_iter/), rather than because the termination
condition /tol/ was satisfied.