diff --git a/mp1/files_data/pagerank1.m b/mp1/files_data/pagerank1.m
index 63d73dd..c3b5862 100644
--- a/mp1/files_data/pagerank1.m
+++ b/mp1/files_data/pagerank1.m
@@ -35,7 +35,7 @@ new_x = x;
 old_norm = -1;
 no = +Inf;
 
-while old_norm == -1 || old_norm > no
+while (old_norm == -1 || old_norm > no) && no > 1e-8
    x = new_x;
    old_norm = no;
    new_x = G * x + e * (z * x);
@@ -44,6 +44,8 @@ while old_norm == -1 || old_norm > no
    no = norm(new_x - x, 2);
 end
 
+display(it); 
+
 % -------------------------------------------------------------------------
 
 % Normalize so that sum(x) == 1.
diff --git a/mp1/files_data/pagerank2.m b/mp1/files_data/pagerank2.m
index 3d4ced6..c974690 100644
--- a/mp1/files_data/pagerank2.m
+++ b/mp1/files_data/pagerank2.m
@@ -32,28 +32,25 @@ x = e/n;
 
 % Check if B will be a singular matrix. If so, change it
 alpha = 1;
-while rcond(A - alpha * I) <= eps
+while rcond(A - alpha * I) < eps
    alpha = alpha + 0.01;
 end
-display(alpha);
-
-B = (A - alpha * I); 
 
 old_x = zeros(n, 1);
 old_norm = -1;
 no = +Inf;
 
 it = 0;
-while old_norm == -1 || old_norm > no
+while (old_norm == -1 || old_norm > no) && no > 1e-8
    old_norm = no;
    old_x = x;
    x = B \ x;
-   x = x/norm(x, 2);
+   x = x/sum(x);
    it = it + 1;
-   no = norm(x - old_x, 2);
+   no = norm(x - old_x, 1);
 end
 
-x = old_x;
+x = abs(old_x);
 display(it); 
 
 % -------------------------------------------------------------------------
diff --git a/mp1/template.pdf b/mp1/template.pdf
index 0c46877..623d90f 100644
Binary files a/mp1/template.pdf and b/mp1/template.pdf differ
diff --git a/mp1/template.tex b/mp1/template.tex
index b3ee529..b753bee 100644
--- a/mp1/template.tex
+++ b/mp1/template.tex
@@ -1,3 +1,4 @@
+% vim: set ts=4 sw=4 et tw=80:
 \documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
 \usepackage{graphicx}
 \usepackage{subcaption}
@@ -10,7 +11,7 @@
 \setduedate{Thursday, 8 October 2020, 12:00 AM}
 
 \serieheader{Numerical Computing}{2020}{Student: Claudio Maggioni}{Discussed with: --}{Solution for Project 1}{}
-\newline
+ewline
 
 \assignmentpolicy
 The purpose of this assignment\footnote{This document is originally based on a SIAM book chapter from \textsl{Numerical Computing with Matlab} from  Clever B. Moler.} is to learn the importance of numerical linear algebra algorithms to solve fundamental  linear algebra problems that occur in search engines.
@@ -82,17 +83,17 @@ Finally, we can always observe a line starting from the top-left of G and ending
 \begin{subfigure}{\textwidth}
 \begin{verbatim}
 
-360    0.0869    31     1    https://creativecommons.org/licenses/by-sa/3.0
+360    0.0869     1    https://creativecommons.org/licenses/by-sa/3.0
 204    0.0406    8      1    https://forum.gitlab.com
-82     0.0189    117    18   https://www.mediawiki.org
-81     0.0188    117    4    https://wikimediafoundation.org
+82     0.01897   https://www.mediawiki.org
+81     0.01887    4    https://wikimediafoundation.org
 87     0.0150    6      1    https://docs.gitea.io
-78     0.0145    114    9    https://www.mediawiki.org/wiki/Special:MyLanguage/
+78     0.01454    9    https://www.mediawiki.org/wiki/Special:MyLanguage/
                                  How_to_contribute
-77     0.0132    77     13   https://foundation.wikimedia.org/wiki/Privacy_policy
-217    0.0127    40     8    https://bugs.archlinux.org
-80     0.0115    107    6    https://foundation.wikimedia.org/wiki/Cookie_statement
-215    0.0114    38     5    https://bbs.archlinux.org
+77     0.0132    https://foundation.wikimedia.org/wiki/Privacy_policy
+217    0.0127     8    https://bugs.archlinux.org
+80     0.01157    6    https://foundation.wikimedia.org/wiki/Cookie_statement
+215    0.0114     5    https://bbs.archlinux.org
 \end{verbatim}
 \caption{Top 10 webpages with highest PageRank}
 \end{subfigure}
@@ -115,18 +116,18 @@ Finally, we can always observe a line starting from the top-left of G and ending
 \begin{subfigure}{\textwidth}
 \begin{verbatim}
 
-411    0.0249    42     1    https://twitter.com/mozilla
-63     0.0248    145    1    https://twitter.com/firefox
-68     0.0203    142    1    https://www.instagram.com/firefox
-412    0.0164    37     1    https://www.instagram.com/mozilla
-62     0.0080    21     1    https://github.com/mozilla/kitsune
-81     0.0070    110    2    https://www.apple.com
+411    0.0249     1    https://twitter.com/mozilla
+63     0.02485    1    https://twitter.com/firefox
+68     0.02032    1    https://www.instagram.com/firefox
+412    0.0164     1    https://www.instagram.com/mozilla
+62     0.0080     1    https://github.com/mozilla/kitsune
+81     0.00700    2    https://www.apple.com
 384    0.0064    5      1    https://www.xfinity.com/privacy/policy/dns
-4      0.0064    32     0    https:
-377    0.0059    19     1    https://abouthome-snippets-service.readthedocs.io/en/
+4      0.0064     0    https:
+377    0.0059     1    https://abouthome-snippets-service.readthedocs.io/en/
                                  latest/data_collection.html
-393    0.0059    19     1    https://www.adjust.com/terms/privacy-policy
-410    0.0057    16     1    https://wiki.mozilla.org/Firefox/Data_Collection
+393    0.0059     1    https://www.adjust.com/terms/privacy-policy
+410    0.0057     1    https://wiki.mozilla.org/Firefox/Data_Collection
 \end{verbatim}
 \caption{Top 10 webpages with highest PageRank}
 \end{subfigure}
@@ -149,16 +150,16 @@ Finally, we can always observe a line starting from the top-left of G and ending
 \begin{subfigure}{\textwidth}
 \begin{verbatim}
 
-55     0.0741    354    1    https://www.instagram.com/usiuniversity
-53     0.0324    366    3    https://www.facebook.com/usiuniversity
+55     0.07414    1    https://www.instagram.com/usiuniversity
+53     0.03246    3    https://www.facebook.com/usiuniversity
 299    0.0248    6      1    https://twitter.com/usi_en
 329    0.0243    8      1    https://www.facebook.com/USIeLab
 308    0.0156    7      3    https://www.facebook.com/USIFinancialCommunication
-60     0.0155    316    2    https://www.swissuniversities.ch
-424    0.0144    96     1    https://it.bul.sbu.usi.ch
+60     0.01556    2    https://www.swissuniversities.ch
+424    0.0144     1    https://it.bul.sbu.usi.ch
 330    0.0123    6      4    https://www.facebook.com/USI.ITDxC
 320    0.0122    7      1    https://www.facebook.com/usiimeg
-56     0.0107    320    0    https://www.youtube.com/usiuniversity
+56     0.01070    0    https://www.youtube.com/usiuniversity
 \end{verbatim}
 \caption{Top 10 webpages with highest PageRank}
 \end{subfigure}
@@ -214,13 +215,25 @@ First we compute the matrix A, finding:
 
 We then find the eigenvectors and eigenvalues of A through MATLAB, finding that the solution of $A x = 1 x$ is:
 
-\[x\approx\begin{bmatrix}
+\[x'\approx\begin{bmatrix}
 	0.4771\\
-    	0.2630\\
-    	0.3747\\
-    	0.4905\\
-    	0.4013\\
-    	0.4013\\
+    0.2630\\
+    0.3747\\
+    0.4905\\
+    0.4013\\
+    0.4013\\
+\end{bmatrix}\]
+
+To obtain more easily interpretable PageRank values, we can require that the sum
+of all PageRanks should be one. Once we normalize in this way, the result is:
+
+\[x=\frac{x'}{\sum_{i=1}^{6}x_i}\approx\begin{bmatrix}
+	0.1981\\
+    0.1092\\
+    0.1556\\
+    0.2037\\
+    0.1667\\
+    0.1667\\
 \end{bmatrix}\]
 
 Thus the pageranks are the components of vector $x$, w.r.t. the order given in U.
@@ -233,5 +246,404 @@ In the computation, increasing $p$ decreases $\delta$ (which represents the prob
 
 \subsection{PageRanks by solving a sparse linear system [50 points]}
 
+\subsubsection{Create \texttt{pagerank1(G)} by modifying \texttt{pagerank.m} to
+use the power method instead of solving thesparse linear system. What is an
+appropriate test for terminating the power iteration?}
 
+The MATLAB solution to this question can be found on
+\texttt{files\_data/pagerank1.m}.
+
+An appropriate termination condition is to stop iterating when the sequence of
+solution vectors stops converging. This can be achieved by checking when, for an
+iteration n
+
+\[||x_n - x_{n-1}|| < ||x_{n-1} - x_{n-2}||\]
+
+stops holding.
+
+Since this condition might be too aggressive for a resonably approximated
+solution, a cutoff value for the norm (say $10^{-8}$) can also be introduced.
+
+\subsubsection{Create \texttt{pagerank2(G)} by modifying \texttt{pagerank.m}
+to use the inverse iteration. Set $\alpha$ equal to 0.8, 0.9 and 1 and comment on
+the different number of iterations they take until convergence.  Also, what
+should be done in the unlikely event that the backslash operation involves a
+division by zero?}
+
+The MATLAB solution to this question can be found on
+\texttt{files\_data/pagerank1.m}.
+
+The termination condition for the previous exercise is used also in this
+implementation.
+
+Iterations are minimal with $\alpha = 1$. For example, for the graph in Figure
+5 in the assignment, we have 5 iterations for $\alpha = 1$, 8 iterations for
+$\alpha=0.9$, and 11 iterations for $\alpha=0.8$.
+
+To avoid divisions by 0 or near-0 numbers we check the reciprocal condition
+number of the matrix $A - \alpha * I$. If this number is below \texttt{eps},
+$\alpha$ must be changed. My implementation simply increases $\alpha$ in increments
+of $10^{-2}$ until a condition number higher than \texttt{eps} is found.
+
+\subsubsection{Use your functions \texttt{pagerank1.m} and \texttt{pagerank2.m}
+(set $\alpha = 1$) to compute the PageRanks of the six-node example presented in
+Figure 1. Make sure you get the correct result from each of your three
+functions.}
+
+Here are the results for \texttt{pagerank1.m}:
+
+\begin{verbatim}
+Using power method implementation
+     page-rank  in  out  url
+   1   0.3210    2    2  alpha
+   6   0.2007    2    1  sigma
+   2   0.1705    1    2  beta
+   4   0.1368    2    1  delta
+   3   0.1066    1    3  gamma
+   5   0.0643    1    0  rho
+\end{verbatim}
+
+And here are the results for \texttt{pagerank2.m}:
+
+\begin{verbatim}
+Using inverse iteration implementation
+     page-rank  in  out  url
+   1   0.3210    2    2  alpha
+   6   0.2007    2    1  sigma
+   2   0.1705    1    2  beta
+   4   0.1368    2    1  delta
+   3   0.1066    1    3  gamma
+   5   0.0643    1    0  rho
+\end{verbatim}
+
+\subsubsection{Use your functions \texttt{pagerank1.m} and \texttt{pagerank2.m}
+(set $\alpha = 1$) to compute the PageRanks of the six-node example presented in
+Figure 5. Discuss the differences between the results obtained now and the ones
+obtained in question 4.}
+
+Here are the results for \texttt{pagerank1.m}:
+
+\begin{verbatim}
+Using power method implementation
+     page-rank  in  out  url
+   4   0.2037    2    1  delta
+   1   0.1981    1    2  alpha
+   5   0.1667    1    1  rho
+   6   0.1667    1    1  sigma
+   3   0.1556    2    1  gamma
+   2   0.1092    1    2  beta
+\end{verbatim}
+
+And here are the results for \texttt{pagerank2.m}:
+
+\begin{verbatim}
+Using inverse iteration implementation
+     page-rank  in  out  url
+   4   0.2037    2    1  delta
+   1   0.1981    1    2  alpha
+   5   0.1667    1    1  rho
+   6   0.1667    1    1  sigma
+   3   0.1556    2    1  gamma
+   2   0.1092    1    2  beta
+\end{verbatim}
+
+Both results are almost identical, with differences in the order of $10^{-8}$
+due to the approximation introduced by the termination conditions. This results
+are also approximately equal to the ones obtained manually once the normalization process
+by the sum of components is applied.
+
+\subsubsection{Use your functions \texttt{pagerank1.m} and \texttt{pagerank2.m}
+(set $\alpha = 1$) to compute the PageRanks of the three selected graphs from
+exercise 2.  Report on the convergence of e.g. the power iteration for these
+subgraphs and summarize the advantage of the power method implemented in
+\texttt{pagerank2.m} against the original implementation in
+\texttt{pagerank.m}.}
+
+In the following outputs, \texttt{it = <number>} represents the number of
+iterations required to compute the PageRanks within the termination criteria
+described before.
+
+Here are the results for \texttt{pagerank1.m} for starting website
+\texttt{http://atelier.inf.usi.ch/\~{}maggicl}:
+\begin{verbatim}
+Using power method implementation
+
+it = 73
+
+     page-rank  in  out  url
+ 360   0.0869   31    1  https://creativecommons.org/licenses/by-sa/3.0
+ 204   0.0406    8    1  https://forum.gitlab.com
+  82   0.0189  117   18  https://www.mediawiki.org
+  81   0.0188  117    4  https://wikimediafoundation.org
+  87   0.0150    6    1  https://docs.gitea.io
+  78   0.0145  114    9  https://www.mediawiki.org/wiki/Special:MyLanguage
+                             /How_to_contribute
+  77   0.0132   77   13  https://foundation.wikimedia.org/wiki/Privacy_policy
+ 217   0.0127   40    8  https://bugs.archlinux.org
+  80   0.0115  107    6  https://foundation.wikimedia.org/wiki/Cookie_statement
+ 215   0.0114   38    5  https://bbs.archlinux.org
+ 216   0.0114   38    8  https://wiki.archlinux.org
+ 218   0.0114   38    6  https://security.archlinux.org
+ 428   0.0107    9    1  https://www.dnb.de/kataloghilfe
+ 219   0.0102   38    7  https://aur.archlinux.org
+ 359   0.0098    9    1  https://creativecommons.org/publicdomain/zero/1.0
+ 366   0.0092   27   21  https://archive.org
+ 446   0.0089   24    5  https://foundation.wikimedia.org/wiki/Terms_of_Use
+  83   0.0079   78    0  https:\/\/schema.org
+  85   0.0074   77    0  https:\/\/www.wikimedia.org\/static\/images
+                             \/wmf-hor-googpub.png
+ 181   0.0066    8    2  https://gitlab.com
+  95   0.0062    2    1  https://www.enable-javascript.com
+ 113   0.0061   13    1  https://www.britannica.com/topic/polenta
+ 429   0.0058    8    1  https://www.dnb.de/EN/Home/home_node.html
+ 432   0.0058    8    1  https://www.dnb.de/expertensuche
+ 417   0.0058    8    1  https://www.dnb.de/DE/Home/home_node.html
+ 379   0.0057   24    2  https://blog.archive.org
+ 213   0.0057   32    7  https://www.archlinux.org
+  99   0.0056    3    1  https://www.usi.ch/it
+  19   0.0051    4    1  https://creativecommons.org/licenses/by-nc-sa/4.0
+ 214   0.0050   31    5  https://www.archlinux.org/packages
+ 220   0.0050   31    6  https://www.archlinux.org/download
+\end{verbatim}
+
+Here are the results for \texttt{pagerank2.m} for starting website
+\texttt{http://atelier.inf.usi.ch/\~{}maggicl}:
+
+\begin{verbatim}
+Using inverse iteration implementation
+
+it = 7
+
+     page-rank  in  out  url
+ 360   0.0869   31    1  https://creativecommons.org/licenses/by-sa/3.0
+ 204   0.0406    8    1  https://forum.gitlab.com
+  82   0.0189  117   18  https://www.mediawiki.org
+  81   0.0188  117    4  https://wikimediafoundation.org
+  87   0.0150    6    1  https://docs.gitea.io
+  78   0.0145  114    9  https://www.mediawiki.org/wiki/Special:MyLanguage
+                             /How_to_contribute
+  77   0.0132   77   13  https://foundation.wikimedia.org/wiki/Privacy_policy
+ 217   0.0127   40    8  https://bugs.archlinux.org
+  80   0.0115  107    6  https://foundation.wikimedia.org/wiki/Cookie_statement
+ 215   0.0114   38    5  https://bbs.archlinux.org
+ 216   0.0114   38    8  https://wiki.archlinux.org
+ 218   0.0114   38    6  https://security.archlinux.org
+ 428   0.0107    9    1  https://www.dnb.de/kataloghilfe
+ 219   0.0102   38    7  https://aur.archlinux.org
+ 359   0.0098    9    1  https://creativecommons.org/publicdomain/zero/1.0
+ 366   0.0092   27   21  https://archive.org
+ 446   0.0089   24    5  https://foundation.wikimedia.org/wiki/Terms_of_Use
+  83   0.0079   78    0  https:\/\/schema.org
+  85   0.0074   77    0  https:\/\/www.wikimedia.org\/static\/images
+                             \/wmf-hor-googpub.png
+ 181   0.0066    8    2  https://gitlab.com
+  95   0.0062    2    1  https://www.enable-javascript.com
+ 113   0.0061   13    1  https://www.britannica.com/topic/polenta
+ 429   0.0058    8    1  https://www.dnb.de/EN/Home/home_node.html
+ 432   0.0058    8    1  https://www.dnb.de/expertensuche
+ 417   0.0058    8    1  https://www.dnb.de/DE/Home/home_node.html
+ 379   0.0057   24    2  https://blog.archive.org
+ 213   0.0057   32    7  https://www.archlinux.org
+  99   0.0056    3    1  https://www.usi.ch/it
+  19   0.0051    4    1  https://creativecommons.org/licenses/by-nc-sa/4.0
+ 220   0.0050   31    6  https://www.archlinux.org/download
+ 214   0.0050   31    5  https://www.archlinux.org/packages
+\end{verbatim}
+
+Here are the results for \texttt{pagerank1.m} for starting website
+\texttt{https://www.iisbadoni.edu.it/}:
+
+\begin{verbatim}
+Using power method implementation
+
+it = 75
+
+     page-rank  in  out  url
+ 411   0.0249   42    1  https://twitter.com/mozilla
+  63   0.0248  145    1  https://twitter.com/firefox
+  68   0.0203  142    1  https://www.instagram.com/firefox
+ 412   0.0164   37    1  https://www.instagram.com/mozilla
+  62   0.0080   21    1  https://github.com/mozilla/kitsune
+  81   0.0070  110    2  https://www.apple.com
+ 384   0.0064    5    1  https://www.xfinity.com/privacy/policy/dns
+   4   0.0064   32    0  https:
+ 377   0.0059   19    1  https://abouthome-snippets-service.readthedocs.io
+                             /en/latest/data_collection.html
+ 393   0.0059   19    1  https://www.adjust.com/terms/privacy-policy
+ 410   0.0057   16    1  https://wiki.mozilla.org/Firefox/Data_Collection
+ 400   0.0057   15    1  https://yandex.ru/legal/confidential
+ 396   0.0057   15    1  https://github.com/mozilla-mobile/firefox-ios
+                             /blob/master/Docs/MMA.md
+   5   0.0056   31    0  https://ssl
+   3   0.0054   36    0  https://www.iisbadoni.edu.it/sites/default/files
+                             /favicon.ico
+   6   0.0054   36    0  https://www.iisbadoni.edu.it/sites/default/files
+                             /logo.png
+ 208   0.0054  159    0  https://schema.org
+  74   0.0052  178    5  https://foundation.mozilla.org
+  72   0.0052   33   32  https://www.mozilla.org/privacy/websites/#cookies
+  23   0.0051    2    1  https://www.iisbadoni.edu.it/mad
+ 300   0.0051  157    0  https://accounts.firefox.com
+\end{verbatim}
+
+Here are the results for \texttt{pagerank2.m} for starting website
+\texttt{https://www.iisbadoni.edu.it}:
+
+\begin{verbatim}
+Using inverse iteration implementation
+
+it = 7
+
+     page-rank  in  out  url
+ 411   0.0249   42    1  https://twitter.com/mozilla
+  63   0.0248  145    1  https://twitter.com/firefox
+  68   0.0203  142    1  https://www.instagram.com/firefox
+ 412   0.0164   37    1  https://www.instagram.com/mozilla
+  62   0.0080   21    1  https://github.com/mozilla/kitsune
+  81   0.0070  110    2  https://www.apple.com
+ 384   0.0064    5    1  https://www.xfinity.com/privacy/policy/dns
+   4   0.0064   32    0  https:
+ 393   0.0059   19    1  https://www.adjust.com/terms/privacy-policy
+ 377   0.0059   19    1  https://abouthome-snippets-service.readthedocs.io
+                             /en/latest/data_collection.html
+ 410   0.0057   16    1  https://wiki.mozilla.org/Firefox/Data_Collection
+ 400   0.0057   15    1  https://yandex.ru/legal/confidential
+ 396   0.0057   15    1  https://github.com/mozilla-mobile/firefox-ios
+                             /blob/master/Docs/MMA.md
+   5   0.0056   31    0  https://ssl
+   3   0.0054   36    0  https://www.iisbadoni.edu.it/sites/default/files
+                             /favicon.ico
+   6   0.0054   36    0  https://www.iisbadoni.edu.it/sites/default/files
+                             /logo.png
+ 208   0.0054  159    0  https://schema.org
+  74   0.0052  178    5  https://foundation.mozilla.org
+  72   0.0052   33   32  https://www.mozilla.org/privacy/websites/#cookies
+  23   0.0051    2    1  https://www.iisbadoni.edu.it/mad
+ 300   0.0051  157    0  https://accounts.firefox.com
+\end{verbatim}
+
+Here are the results for \texttt{pagerank1.m} for starting website
+\texttt{https://www.usi.ch}:
+
+\begin{verbatim}
+Using power method implementation
+
+it = 66
+
+     page-rank  in  out  url
+  55   0.0741  354    1  https://www.instagram.com/usiuniversity
+  53   0.0324  366    3  https://www.facebook.com/usiuniversity
+ 299   0.0248    6    1  https://twitter.com/usi_en
+ 329   0.0243    8    1  https://www.facebook.com/USIeLab
+ 308   0.0156    7    3  https://www.facebook.com/USIFinancialCommunication
+  60   0.0155  316    2  https://www.swissuniversities.ch
+ 424   0.0144   96    1  https://it.bul.sbu.usi.ch
+ 330   0.0123    6    4  https://www.facebook.com/USI.ITDxC
+ 320   0.0122    7    1  https://www.facebook.com/usiimeg
+  56   0.0107  320    0  https://www.youtube.com/usiuniversity
+   5   0.0096  317   71  https://usi.ch
+  62   0.0090  319   18  https://search.usi.ch
+ 337   0.0087    7    1  https://twitter.com/usisoftware
+  63   0.0080  303   19  https://desk.usi.ch
+ 130   0.0077   25    0  https://www.swissuniversities.ch/it
+  54   0.0072  208    0  https://twitter.com/USI_university
+ 323   0.0066    9    5  https://www.facebook.com/usiorientamento
+ 150   0.0062   12    1  https://www.innosuisse.ch/inno/it/home.html
+ 248   0.0061   10    1  https://www.facebook.com/usimdfc
+ 106   0.0060  132    8  https://newsletter.usi.ch/archive/en
+ 135   0.0057  201    0  https://schema.org
+ 326   0.0057    6    1  https://www.facebook.com/usialloggimendrisio
+ 322   0.0055    6    1  https://www.facebook.com/USImem
+ 366   0.0054    6    1  https://www.instagram.com/usi_ics_lugano
+ 212   0.0054   12    3  https://www.facebook.com/usimt
+   7   0.0051  211   32  https://search.usi.ch/it
+   6   0.0051  204    0  https://www.usi.ch/sites/all/themes/usiclean
+                             /img/bollino-usi.svg
+  14   0.0051  204   62  https://www.usi.ch/originalnode/342
+  15   0.0051  204   57  https://www.usi.ch/originalnode/358
+  16   0.0051  204   62  https://www.usi.ch/originalnode/343
+  17   0.0051  204   57  https://www.usi.ch/originalnode/344
+  18   0.0051  204   58  https://www.usi.ch/en/originalnode/12174
+  20   0.0051  204   60  https://www.usi.ch/originalnode/349
+  21   0.0051  204   62  https://www.usi.ch/originalnode/8996
+  22   0.0051  204   60  https://www.usi.ch/originalnode/348
+  23   0.0051  204   59  https://www.usi.ch/originalnode/351
+  24   0.0051  204   58  https://www.usi.ch/originalnode/350
+  25   0.0051  204   61  https://www.usi.ch/originalnode/353
+  26   0.0051  204   58  https://www.usi.ch/en/originalnode/354
+  27   0.0051  204   59  https://www.usi.ch/originalnode/8014
+  61   0.0051  204    0  https://www.usi.ch/sites/all/themes/usiclean
+                             /img/swissuniversities.svg
+  57   0.0050  188    9  https://newsletter.usi.ch/archive
+\end{verbatim}
+
+Here are the results for \texttt{pagerank2.m} for starting website
+\texttt{https://www.usi.ch}:
+
+\begin{verbatim}
+Using inverse iteration implementation
+
+it = 7
+
+     page-rank  in  out  url
+  55   0.0741  354    1  https://www.instagram.com/usiuniversity
+  53   0.0324  366    3  https://www.facebook.com/usiuniversity
+ 299   0.0248    6    1  https://twitter.com/usi_en
+ 329   0.0243    8    1  https://www.facebook.com/USIeLab
+ 308   0.0156    7    3  https://www.facebook.com/USIFinancialCommunication
+  60   0.0155  316    2  https://www.swissuniversities.ch
+ 424   0.0144   96    1  https://it.bul.sbu.usi.ch
+ 330   0.0123    6    4  https://www.facebook.com/USI.ITDxC
+ 320   0.0122    7    1  https://www.facebook.com/usiimeg
+  56   0.0107  320    0  https://www.youtube.com/usiuniversity
+   5   0.0096  317   71  https://usi.ch
+  62   0.0090  319   18  https://search.usi.ch
+ 337   0.0087    7    1  https://twitter.com/usisoftware
+  63   0.0080  303   19  https://desk.usi.ch
+ 130   0.0077   25    0  https://www.swissuniversities.ch/it
+  54   0.0072  208    0  https://twitter.com/USI_university
+ 323   0.0066    9    5  https://www.facebook.com/usiorientamento
+ 150   0.0062   12    1  https://www.innosuisse.ch/inno/it/home.html
+ 248   0.0061   10    1  https://www.facebook.com/usimdfc
+ 106   0.0060  132    8  https://newsletter.usi.ch/archive/en
+ 135   0.0057  201    0  https://schema.org
+ 326   0.0057    6    1  https://www.facebook.com/usialloggimendrisio
+ 322   0.0055    6    1  https://www.facebook.com/USImem
+ 366   0.0054    6    1  https://www.instagram.com/usi_ics_lugano
+ 212   0.0054   12    3  https://www.facebook.com/usimt
+   7   0.0051  211   32  https://search.usi.ch/it
+  14   0.0051  204   62  https://www.usi.ch/originalnode/342
+  27   0.0051  204   59  https://www.usi.ch/originalnode/8014
+  21   0.0051  204   62  https://www.usi.ch/originalnode/8996
+  22   0.0051  204   60  https://www.usi.ch/originalnode/348
+  25   0.0051  204   61  https://www.usi.ch/originalnode/353
+  61   0.0051  204    0  https://www.usi.ch/sites/all/themes/usiclean
+                             /img/swissuniversities.svg
+  16   0.0051  204   62  https://www.usi.ch/originalnode/343
+  23   0.0051  204   59  https://www.usi.ch/originalnode/351
+  15   0.0051  204   57  https://www.usi.ch/originalnode/358
+  17   0.0051  204   57  https://www.usi.ch/originalnode/344
+  24   0.0051  204   58  https://www.usi.ch/originalnode/350
+   6   0.0051  204    0  https://www.usi.ch/sites/all/themes/usiclean
+                             /img/bollino-usi.svg
+  20   0.0051  204   60  https://www.usi.ch/originalnode/349
+  26   0.0051  204   58  https://www.usi.ch/en/originalnode/354
+  18   0.0051  204   58  https://www.usi.ch/en/originalnode/12174
+  57   0.0050  188    9  https://newsletter.usi.ch/archive
+\end{verbatim}
+
+The potential of the algorithm in \texttt{pagerank2.m} compared to the one in
+\texttt{pagerank.m} is that by using inverse iteration, thus theoretically
+avoiding a full matrix system solution process, the sparsity of matrix G can be
+maintained during the computation thus saving memory costs.
+
+However, since my \texttt{pagerank2.m} implementation is a simplified
+implementation of the algorithm and indeed uses system solution
+(MATLAB's \texttt{mldivide}), this
+theoretical advantages are voided: my implementation is 3 times as long as the
+original one and uses approximately the same amount of memory. Advantages over
+\texttt{pagerank1.m} (due to the intentionally increased rate of convergence)
+are clear: in
+all the examples above, the inverse iteration implementation is at least 8 times
+faster than the ``vanilla'' power method.
 \end{document}