Über näherungsweise Auflösung von Systemen homogener linearer Gleichungen

Summary

If a singularn×n-matrixS is approximated byS+A, an approximation to a non-trivial solution ofSζ′=0 is obtained from a solution ξ of (S+ A)_ξ′=η′ in forming ξ/|ξ|. The vector η is here a conveniently chosen constant vector, and the error is, ifA=(a _μv ),

$$O\left( {\sqrt {\mathop \sum \limits_{\mu , \nu } |a_{\mu \nu } |^2 } } \right).$$