Abstract
The paper is concerned with the stability of the L ∞ -quasi-solutions In the sense of IVANOV for overdetermined, ill-conditioned linear equation systems. A stability theorem is proved, which considers perturbations in the coefficient-matrix of the equation system. Then an efficient way for the computation of L ∞-quasi-solutions is shown by means of parametric linear programming. The numerical investigations performed allow statements on the stability behaviour of such solutions when the right-hand side and the matrix of the equation systema reperturbed. It is shown that L ∞-quasi-solutions just provide good approximations if Euclidean-quasi-solutions or equivalent regularized solutions are very imprecisely.
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