Autor:

Benci, Vieri ; Cococcioni, Marco ; Fiaschi, Lorenzo

Współtwórca:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Tytuł:

Non-standard analysis revisited: An easy axiomatic presentation oriented towards numerical applications

Tytuł publikacji grupowej:

AMCS, volume 32 (2022)

Temat i słowa kluczowe:

Alpha-Theory ; non-standard analysis ; non-Archimedean analysis ; algorithmic numbers ; non-Archimedean scientific computing

Abstract:

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. ; 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.

Wydawca:

Zielona Góra: Uniwersytet Zielonogórski

Data wydania:

2022

Typ zasobu:

artykuł

DOI:

10.34768/amcs-2022-0006

Strony:

65-80

Źródło:

AMCS, volume 32, number 1 (2022) ; kliknij tutaj, żeby przejść

Jezyk:

eng

Licencja CC BY 4.0:

kliknij tutaj, żeby przejść

Prawa do dysponowania publikacją:

Biblioteka Uniwersytetu Zielonogórskiego