3rd ENOC ProceedingsIndex



Generalized normal solution of degenerated system of equations/inequalities

Vladimir K. Gorbunov


MathMech Faculty
Ulianovsk State University
L.Tolstoy str.42, USU, 432700 Ulyanovsk
Russia



Abstract


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.


Document


Gorbunov.ps.gz

Gorbunov.pdf


Contact information


Vladimir K. Gorbunov

MathMech Faculty
Ulianovsk State University
L.Tolstoy str.42, USU, 432700 Ulyanovsk
Russia

e-mail: gorbunov@cpm.univ.simbirsk.su



3rd ENOC ProceedingsIndex