From b60937ccf6c90a288395e9f8fb28efc9b6f824ba Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Marcus=20Thelander=20Andr=C3=A9n?=
 <marcus.thelander_andren@control.lth.se>
Date: Fri, 22 Sep 2017 10:53:43 +0200
Subject: [PATCH] Update README.md

---
 README.md | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/README.md b/README.md
index 5f3fedf..e9b279e 100644
--- a/README.md
+++ b/README.md
@@ -65,6 +65,21 @@ The input arguments of `optimal_bound_2D` are:
 * `plot_progress` : Specifies if $`V`$ and $`\partial \Omega`$ should be plotted during the simulation (`plot_progress = 1`) or not (`plot_progress = 0`).
 * `print_progress` : Specifies if iteration info should be printed to the command window during the simulation (`print_progress = 1`) or not (`print_progress = 0`).
 
+The output argument `V` is a matrix with dimensions compatible with `x1vec`and `x2vec`. For instance, you can call `surf(x1vec, x2vec, V)` to generate a surface plot of $`V`$, or
+`contour(x1vec, x2vec, V, [0 0])` to plot the bound $`\partial \Omega`$.
+
+## Plotting during Simulation
+With the input argument `plot_progress = 1`, a surface plot of $`V`$ and a plot of $`\partial \Omega`$ will be updated every 10th iteration of the simulation.
+
+
+## Printing during Simulation
+With the input argument `print_progress = 1`, information of every 10th iteration will be printed to the command window during the simulation. An example is shown below:
+
+```matlab
+Iterations : 10 out of 50000 | Maximum Vdiff = 0.00049488 | V(0) = -0.0049714
+```
+The printout displays the current iteration number (in this case 10) out of the maximum number of iterations (50000). The `Maximum Vdiff` value is the largest absolute value between the current and last iteration
+$`V`$, and is the basis for determining when stationarity is reached. The value $`V(0)`$ is the current value of $`V`$ at the origin. It is linked to the per-sample cost $`\rho`$, as $`V(0) = -\rho`$ (see the [article](cdc2017_paper.pdf)).
 # About the Numerical Method
 The numerical solution method is based on simulating the non-stationary version of the PDE using finite-difference approximations of the differential operators and gridding in time and space. 
 In this implementation, we use the backward-time central-space (BTCS) finite-difference approximation (see e.g. this [article](http://depa.fquim.unam.mx/amyd/archivero/DiferenciasFinitas4_25730.pdf) for more details).
-- 
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