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authorLeonard Kugis <leonard@kug.is>2020-04-21 00:34:24 +0200
committerLeonard Kugis <leonard@kug.is>2020-04-21 00:34:24 +0200
commitf65ec3a75070feb4f19ed64b1afade68f50e6456 (patch)
tree98f65337c6ffe3f9513d6a024656f8462748484f
parent78a6bf5c184e850cbbc4e17a82104d0d7a8bcf11 (diff)
Numerical Mathematics
Begin
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-/output/
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+*.jpg
# Created by https://www.gitignore.io/api/vim,linux,latex
# Edit at https://www.gitignore.io/?templates=vim,linux,latex
diff --git a/README.md b/README.md
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# 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
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+# 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
+
+$$
+K_r^c=||||
+$$