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Mathematics-Online problems:

Interactive Problem 18: Linear Iterative Methods

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Make one iteration step of the Jacobi- respectively Gauß-Seidel-Method for the LSE

$\displaystyle \left[ \begin{array}{cc} 2 & a \\ 1 & 2 \end{array} \right] \left... ...\\ x_2 \end{array} \right]= \left[ \begin{array}{c} 4 \\ 8 \end{array} \right] $

with initial value $ X_{0}=[1,0]^t$. Find the parameter $ a\in \mathbb{R}$ for which the iteration is convergent.


Solution:

Jacobi-Iteration:
$ X_{1}=\frac{1}{2}\Big[$ , $ \Big]^{\operatorname t}$,     $ \vert a\vert<$ .

Gauß-Seidel-Iteration:
$ X_{1}=\Big[$ , $ \Big]^{\operatorname t}$,     $ \vert a\vert<$ .

   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 8/11/2017