Mathematics-Online lexicon: Approximative Solution of Over-Determined Linear Systems of Equations

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	Mathematics-Online lexicon:
	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

of a given LSE

$\displaystyle Ax=b$

with $m\times n$ -coefficient matrix

is not contained in the linear hull of the columns of the coefficient matrix

(as is often the case for

), 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)

see also:

Keyword: System of equations, linear: least squares problem

automatically generated 2/ 8/2005