Various documentation fixes from William Rucklidge.
Change-Id: I102e98f41f4b5fe2a84d1224d5ed7517fdfdb022
diff --git a/docs/source/modeling.rst b/docs/source/modeling.rst
index 5fff351..21cda70 100644
--- a/docs/source/modeling.rst
+++ b/docs/source/modeling.rst
@@ -43,7 +43,7 @@
outliers on the solution of non-linear least squares problems.
:math:`l_j` and :math:`u_j` are lower and upper bounds on the
-:math:parameter block `x_j`.
+parameter block :math:`x_j`.
As a special case, when :math:`\rho_i(x) = x`, i.e., the identity
function, and :math:`l_j = -\infty` and :math:`u_j = \infty` we get
@@ -1462,7 +1462,7 @@
.. function bool Problem::HasParameterBlock(const double* values) const;
- Is the give parameter block present in the problem or not?
+ Is the given parameter block present in the problem or not?
.. function void Problem::GetParameterBlocks(vector<double*>* parameter_blocks) const
diff --git a/docs/source/solving.rst b/docs/source/solving.rst
index 4d091a3..1b52c02 100644
--- a/docs/source/solving.rst
+++ b/docs/source/solving.rst
@@ -27,13 +27,18 @@
L \le x \le U
:label: nonlinsq
-Here, the Jacobian :math:`J(x)` of :math:`F(x)` is an :math:`m\times
-n` matrix, where :math:`J_{ij}(x) = \partial_j f_i(x)` and the
-gradient vector :math:`g(x) = \nabla \frac{1}{2}\|F(x)\|^2 = J(x)^\top
-F(x)`. Since the efficient global minimization of :eq:`nonlinsq` for
+Where, :math:`L` and :math:`U` are lower and upper bounds on the
+parameter vector :math:`x`.
+
+Since the efficient global minimization of :eq:`nonlinsq` for
general :math:`F(x)` is an intractable problem, we will have to settle
for finding a local minimum.
+In the following, the Jacobian :math:`J(x)` of :math:`F(x)` is an
+:math:`m\times n` matrix, where :math:`J_{ij}(x) = \partial_j f_i(x)`
+and the gradient vector is :math:`g(x) = \nabla \frac{1}{2}\|F(x)\|^2
+= J(x)^\top F(x)`.
+
The general strategy when solving non-linear optimization problems is
to solve a sequence of approximations to the original problem
[NocedalWright]_. At each iteration, the approximation is solved to
@@ -118,7 +123,7 @@
giving rise to a different concrete trust-region algorithm. Currently
Ceres, implements two trust-region algorithms - Levenberg-Marquardt
and Dogleg, each of which is augmented with a line search if bounds
-constrained are present [Kanzow]_. The user can choose between them by
+constraints are present [Kanzow]_. The user can choose between them by
setting :member:`Solver::Options::trust_region_strategy_type`.
.. rubric:: Footnotes
