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Approximative Solution of Over-Determined Linear Systems of Equations

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 overview
If the right hand side $ b$ of a given LSE

$\displaystyle Ax=b $

with $ m\times n$-coefficient matrix $ A$ is not contained in the linear hull of the columns of the coefficient matrix $ A$ (as is often the case for $ m>n$), that is, if

   Rang$\displaystyle (A) <$   Rang$\displaystyle \left([A,b]\right)\, , $

then the LSE has no solution. The LSE is a so called over-determined system. In this case it is possible to find an approximative solution by solving the approximation problem

$\displaystyle \Vert Ax-b \Vert _2 \to \min\,. $

(Authors: App/Burkhardt/Höllig)
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  automatically generated 2/ 8/2005