Reformulate some sentences

Change-Id: I4841aa8e8522008dd816261d9ad98e5fb8ad1758
This commit is contained in:
Carl Dehlin
2020-06-15 20:01:18 +02:00
parent 8ac6655ce8
commit 27cab77b69
+4 -5
View File
@@ -1152,8 +1152,7 @@ their shape graphically. More details can be found in
Theory
------
Let us consider a problem with a single problem and a single parameter
block.
Let us consider a problem with a single parameter block.
.. math::
@@ -1171,8 +1170,8 @@ where the terms involving the second derivatives of :math:`f(x)` have
been ignored. Note that :math:`H(x)` is indefinite if
:math:`\rho''f(x)^\top f(x) + \frac{1}{2}\rho' < 0`. If this is not
the case, then its possible to re-weight the residual and the Jacobian
matrix such that the corresponding linear least squares problem for
the robustified Gauss-Newton step.
matrix such that the robustified Gauss-Newton step corresponds to an
ordinary linear least squares problem.
Let :math:`\alpha` be a root of
@@ -1193,7 +1192,7 @@ In the case :math:`2 \rho''\left\|f(x)\right\|^2 + \rho' \lesssim 0`,
we limit :math:`\alpha \le 1- \epsilon` for some small
:math:`\epsilon`. For more details see [Triggs]_.
With this simple rescaling, one can use any Jacobian based non-linear
With this simple rescaling, one can apply any Jacobian based non-linear
least squares algorithm to robustified non-linear least squares
problems.