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Approximation, solution operators and quantale-valued metrics

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dc.abstract.enA generalized solution operator is a mapping abstractly describing a computational problem and its approximate solutions. It assigns a set of ε-approximations of a solution to the problem instance f and accuracy of approximation ε. In this paper we study generalized solution operators for which the accuracy of approximation is described by elements of a complete lattice equipped with a compatible monoid structure, namely, a quantale. We provide examples of computational problems for which the accuracy of approximation of a solution is measured by such objects. We show that the sets of ε-approximations are, roughly, closed balls with radii ε with respect to a certain family of quantale-valued generalized metrics induced by a generalized solution operator.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorSiedlecki, Paweł
dc.date.accessioned2024-01-24T16:55:19Z
dc.date.available2024-01-24T16:55:19Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number4
dc.description.volume91
dc.identifier.doi10.1007/S00010-017-0485-8
dc.identifier.issn0001-9054
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101058
dc.languagepol
dc.pbn.affiliationmathemathics
dc.relation.ispartofAequationes Mathematicae
dc.relation.pages745–758
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleApproximation, solution operators and quantale-valued metrics
dc.typeJournalArticle
dspace.entity.typePublication