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<dc:title xml:lang="pl"><![CDATA[Non-standard analysis revisited: An easy axiomatic presentation oriented towards numerical applications]]></dc:title>
<dc:creator><![CDATA[Benci, Vieri]]></dc:creator>
<dc:creator><![CDATA[Cococcioni, Marco]]></dc:creator>
<dc:creator><![CDATA[Fiaschi, Lorenzo]]></dc:creator>
<dc:subject xml:lang="pl"><![CDATA[Alpha-Theory]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[non-standard analysis]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[non-Archimedean analysis]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[algorithmic numbers]]></dc:subject>
<dc:subject xml:lang="pl"><![CDATA[non-Archimedean scientific computing]]></dc:subject>
<dc:description xml:lang="pl"><![CDATA[Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson`s non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory.]]></dc:description>
<dc:description xml:lang="pl"><![CDATA[To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases.]]></dc:description>
<dc:publisher><![CDATA[Zielona Góra: Uniwersytet Zielonogórski]]></dc:publisher>
<dc:contributor><![CDATA[Korbicz, Józef (1951- ) - red.]]></dc:contributor>
<dc:contributor><![CDATA[Uciński, Dariusz - red.]]></dc:contributor>
<dc:date><![CDATA[2022]]></dc:date>
<dc:type xml:lang="pl"><![CDATA[artykuł]]></dc:type>
<dc:identifier><![CDATA[http://www.zbc.uz.zgora.pl/repozytorium/Content/86372/AMCS_2022_32_1_6.pdf]]></dc:identifier>
<dc:identifier><![CDATA[https://zbc.uz.zgora.pl/repozytorium/dlibra/publication/101430/edition/86372/content]]></dc:identifier>
<dc:identifier><![CDATA[oai:zbc.uz.zgora.pl:86372]]></dc:identifier>
<dc:source xml:lang="pl"><![CDATA[AMCS, volume 32, number 1 (2022)]]></dc:source>
<dc:source xml:lang="pl"><![CDATA[https://www.amcs.uz.zgora.pl/?action=papers&issue=123]]></dc:source>
<dc:language><![CDATA[eng]]></dc:language>
<dc:relation><![CDATA[oai:zbc.uz.zgora.pl:publication:101430]]></dc:relation>
<dc:rights xml:lang="pl"><![CDATA[Biblioteka Uniwersytetu Zielonogórskiego]]></dc:rights>
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