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| -rw-r--r-- | .gitignore | 3 | ||||
| -rw-r--r-- | README.md | 28 | ||||
| -rw-r--r-- | en_GB/Numerical Mathematics/numerical_mathematics.md | 33 |
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@@ -1,4 +1,5 @@ -/output/ +*output/* +*.jpg # Created by https://www.gitignore.io/api/vim,linux,latex # Edit at https://www.gitignore.io/?templates=vim,linux,latex @@ -1,13 +1,30 @@ # Lernzettel +## Über das Projekt + +Dies ist eine Sammlung meiner Lernzettel für diverse Kurse. +Da es ein Projekt von Studenten für Studenten ist, besteht keine Garantie auf Korrektheit oder Vollständigkeit. + +## About + +This is a collection of my digital lecture summaries. +This being a full project by students for students, there is no guarantee for correctness and completeness. + ## Inhaltsverzeichnis ### Einführung in die Informationssicherheit -- [Source](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md) -- [HTML](http://encrox.com/introduction_to_information_security.html) +- [Quelldaten](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md) +- [HTML](http://encrox.com/projects/lernzettel/introduction_to_information_security.html) - [PDF](http://encrox.com/introduction_to_information_security.pdf) +### Numerische Mathematik + +- [Quelldaten](en_GB/Numerical Mathematics/numerical_mathematics.md) +- [HTML](http://encrox.com/numerical_mathematics.html) +- [PDF](http://encrox.com/numerical_mathematics.pdf) +- [Klausurzettel](en_GB/Numerical Mathematics/cheatsheet.jpg) + ## Table of contents ### Introduction to Information Security @@ -15,3 +32,10 @@ - [Source](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md) - [HTML](http://encrox.com/introduction_to_information_security.html) - [PDF](http://encrox.com/introduction_to_information_security.pdf) + +### Numerical Mathematics + +- [Source](en_GB/Numerical Mathematics/numerical_mathematics.md) +- [HTML](http://encrox.com/numerical_mathematics.html) +- [PDF](http://encrox.com/numerical_mathematics.pdf) +- [Cheatsheet](en_GB/Numerical Mathematics/cheatsheet.jpg) diff --git a/en_GB/Numerical Mathematics/numerical_mathematics.md b/en_GB/Numerical Mathematics/numerical_mathematics.md new file mode 100644 index 0000000..01ff084 --- /dev/null +++ b/en_GB/Numerical Mathematics/numerical_mathematics.md @@ -0,0 +1,33 @@ +# Numerical Mathematics + +## Operator Norm + +$$ +||F||=\sup\limits_{x\neq0}\frac{||F(x)||_w}{||x||_v}=\sup\limits_{||x||_v=1}||F(x)||_w +$$ + +## Condition numbers + +$K_a := Absolute condition number$ + +$K_r := Relative conditioon number$ + +### Operator linear + +$$ +K_a=||F||_{v,w}\in[0, \infin[ +K_r\leq\frac{||F||_{v,w}}{\inf\limits_{||x||_v=1}||F(x)||_w}\in[0,\infin[ +$$ + +### F, A bijektive + +$$ +K_r\leq||F||_{v,w}||F^{-1}||_{v,w} +K_r(A)=||A||_\infin||A^{-1}||_\infin +$$ + +### Component based + +$$ +K_r^c=|||| +$$ |