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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
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tree98f65337c6ffe3f9513d6a024656f8462748484f /en_GB/Numerical Mathematics/numerical_mathematics.md
parent78a6bf5c184e850cbbc4e17a82104d0d7a8bcf11 (diff)
Numerical Mathematics
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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
+
+$$
+K_r^c=||||
+$$