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The regularization problem of degenerated system of equations/inequalities
in Banach spaces is considered. Our approach is based on the explicit
parametrization of input data and on the utilization of the multy-valued
mapping techniques. We suggest an extended minimization method that resolves
both regularization and data correction problems simultaneously. According to
the method an ill-posed problem should be replaced by a search of the minimal
norm element in the join of solution sets of the family of problems that are
equivalent to the initial one with respect to input data accuracy. We named
this element as generalized normal solution (GNS) of a given ill-posed
problem. Theoretical results on regularization property of this method as well
as problems of its approximation and numeric implementations via linearization
and normal spline collocation methods are presented here.
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