diff --git a/mp1/project.1.Maggioni.Claudio.tex b/mp1/project.1.Maggioni.Claudio.tex index ab1dd77..e0321bc 100644 --- a/mp1/project.1.Maggioni.Claudio.tex +++ b/mp1/project.1.Maggioni.Claudio.tex @@ -104,7 +104,13 @@ By choosing $\alpha$ close to $\lambda_1$, the convergence is sped up. To furthe \subsubsection{What is the difference in cost of a single iteration of the power method, compared to the inverse iteration?} -Inverse iteration is generally more expensive than a regular application of the power method, due to the overhead caused by the intermediate matrix B. One must either recompute B every time $\alpha$ changes, which is rather expensive due to the inverse operation in the definition of B, or one must solve the matrix equation $(A - \alpha I)v_k = v_{k-1}$ in every iteration. +Inverse iteration is generally more expensive than a regular application of the +power method, due to the fact that the computation is based on the solution of a +linear system, which compared to the matrix vector multiplication performed by +the power method it is quite expensive. One must either recompute B every time +$\alpha$ changes, which is rather expensive due to the inverse operation in the +definition of B, or one must solve the matrix equation +$(A - \alpha I)v_k = v_{k-1}$ in every iteration. \subsubsection{What is a Rayleigh quotient and how can it be used for eigenvalue computations?} @@ -140,10 +146,10 @@ Finally, we can always observe a line starting from the top-left of G and ending \begin{verbatim} 360 0.0869 1 https://creativecommons.org/licenses/by-sa/3.0 -204 0.0406 8 1 https://forum.gitlab.com +204 0.0406 8 1 https://forum.gitlab.com 82 0.01897 https://www.mediawiki.org 81 0.01887 4 https://wikimediafoundation.org -87 0.0150 6 1 https://docs.gitea.io +87 0.0150 6 1 https://docs.gitea.io 78 0.01454 9 https://www.mediawiki.org/wiki/Special:MyLanguage/ How_to_contribute 77 0.0132 https://foundation.wikimedia.org/wiki/Privacy_policy @@ -696,7 +702,7 @@ 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 +theoretical advantages are voided: my implementation takes 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 diff --git a/mp2/submit.sh b/mp2/submit.sh new file mode 100755 index 0000000..a7ac16d --- /dev/null +++ b/mp2/submit.sh @@ -0,0 +1,9 @@ +#!/bin/sh + +PID="2" +dname="Project.$PID.Maggioni.Claudio" +zname="project.$PID.Maggioni.Claudio" + +rm -v $zname.zip +zip $zname.zip ex*.tex $zname.{pdf,tex} $dname/ex?.m $dname/example.m $dname/degcentrality.m \ + $dname/pagerank.m 1_*.pdf